Some scientists argue that probabilistic formulations are fudge factors for systems we don't completely understand, systems with hidden or latent variables, & that a "complete theory" would provide ways to account for all observable phenomena & thus avoid any indeterminism.
Einstein objected to the probabilistic nature of quantum mechanics, declaring famously, "I am convinced God does not play dice." Einstein was a big fan of hidden variables.
Hidden variables can correspond to physical reality or abstract concepts.
Take the political system. A discussion of Harry Reid's little green men or his role in the Nevada Bernie-vs-Hillary primary might benefit from considering hidden variable theory. As would the shock (Strzok!) of Comey's nolle prosequi and Hillary's electoral loss.
Strzok's 100-million margin-of-victory was, I suspect, a greater —if inverse—indicator of the eventual outcome than The Times' more reasonable-sounding expressions of near-certainty.
2
A probability of one in a hundred doesn't mean never. It means it will happen and the might turn out to be ten years from now or next year... especially if the model for your probability is wrong.
2
Mr. Leonhardt, you should probably round to zero your estimate of how much Russia impacted the election. And while your ar at it, round up to 100% how wrong you have been about Trump.
5
First of all, the headline is false advertising: Leonhardt has not told the readers
what he got wrong.
Second, in his bis "example", he has not distinguished between a ten percent increase (say, from 10% to 11% (which is a 10% increase in the probablility), an increase in the percent probability of 10 percentage points (say, from 10% to 20%), and the completely unrealistic notion that the statement is equivalent of an increase from 0 to 10 (which would be an infinite increase).
9
There was only a small percentage chance that the Times' printing excerpts from "Clinton Cash" and harping on the email non-scandal would through the election to a nationalistic lunatic, but hey, long shots come in sometimes. Put that into a story, dude.
5
GIGO
Garbage In Garbage Out
It applies to statisticians just as it does to the rest of us. Use the wrong data set and your "statistics" are worthless.
5
The problem with probabilities is when you read your own tea leaves you probably go wrong.
1
On probabilities of election outcomes: In the last election i voted for Clinton in a state that was going to vote overwhelmingly for her. I might have stayed home, but i went to the polls to vote FOR Kamala Harris. Years before, in one of those rare news interviews (and on Fox), she had come across as a prosecutor who was sincere about going after crime that needed to be prosecuted (i forget now whether it was against children, women, or corruption in the sherrif's office--maybe all three). In Alabama recently Black voters came out overwhelmingly to vote for a man that had prosecuted KKK murderers. The point here, and especially for the Democrats, voter turnout is what matters. They need candidates that voters will identify with and make the effort to vote for, not the lessor of two evils or some political hack with only strong name identity. One other thing, Republican gerrymandering has resulted in some of their safe districts now being in play as voters realize Republicans have thrown in their lot with KKK racists, neoNazis, pedophiles and a dishonest president who has only two goals, to stay out of jail for fraud and past financial crimes and to continue to enrich himself. That 32% (63% of white women in AL) of the electorate approve of this--the same 32% btw, the Bush torture crowd, who stuck with him after 2 failed wars and the financial meltdown--is all the more reason for the Democrats to get good candidates and work to turn out their vote. The 32% do vote.
2
New rule: A statement isn't a fact because this administration keeps repeating it. The Times has been holding the administration accountable and deserves praise for the tremendous work all year of speaking truth to power!
4
I don’t know even know why this column is even necessary. Every one was wrong this year and every one knows it
2
I recall a Democratometer on election night. Like a spedometer, it started at ‘sure thing’ and sank towards ‘still very likely’ as the NYT floundered in forecasting ineptitude.
Twas not the public’s failure to understand probability.
Mea culpa columns are generally only useful when those applying them have owned up.
I would say that this column should come with error bars. very large ones.
Probability that the authors understand what happened. 50%, +/- 50%.
3
A good rule of thumb: listen to Gil Welch. I had the privilege of working with him for 13 years, and I’ve never encountered a better thinker, even among his incredibly smart and accomplished colleagues at Dartmouth.
SINGLE STATISTICS Are static, while the course of events is dynamic--ever changing. Any single statistic is limited by the amount of information about how it was calculated. For example, the weather forecast says that there is a 10% chance of precipitation. How do we know that? Because the weather satellites broadcast images of weather fronts and their motions on maps of the US, for example. Relying upon a single number is impossible. There are always mitigating factors. Though the NRA disagrees vehemently with this observation, the fact is that ALL shootings are dependent upon access to firearms. The proof is that in states where access to firearms is more strictly enforced, there is a lower rate of shootings. While in states where firearms are more readily available, there tends to be a higher rate of shootings. But there are unpredictable factors, such as a serial killer driving through an area on a killing spree. Other factors are important as well, since domestic violence, including shootings, increases when there are family conflicts where someone is under the influence of alcohol or drugs. That's often unpredictable, depending on whether someone comes home under the influence, or gets high at home from using alcohol or drugs. Hillary, for example, won the popular vote by more than 2.8 million. But Trump won a majority of 70+ votes in the electoral college. So as we know all to well, he's in the Oral Office or at Mar a Lego. Numbers on his tax returns anyone?
2
Interesting but incorrect idea. Most things that are currently reported with a probability don't really have enough data to make a good estimate. That is why they fail so many times. Of course it is also true that no matter how unlikely some things do happen. Now with say a card game we have full data, but with say weather or elections not nearly so good. Remember GIGO!!
3
I don't think that Obama played the odds in his decision to defer discussion of Russian interference in the election process. Who would make that calculation when our current president seemed to be overshadowing the primaries. Instead, I believe he was trying to avoid creating the impression that he was trying to influence the election. Remember - Trump's allegations of "fake news" were on his lips whenever he didn't like the coverage, which is almost laughable since he is the embodiment of fake news.
15
I would not want a "discussion" but rather just the facts. Now the facts as I understand them are that individuals or groups associated with Russia did many things to disrupt our society. That we have a free society allowed them to do so. I seem to remember Obama interfering in an election in Israel some time ago.
3
Unmentioned are the assumptions behind the probabilities. What distribution is being used? Nicholas Taleb has written several books, including "the Black Swan" and "Fooled by Randomness" that bemoan the use of the Gaussian distribution where it has no place, especially in financial markets but in much of human interactions. It does not provide sufficient allowance for extremely rare events but wrong or not, the math is so nice and elegant, the integrals so concise, that it has become irresistible.The result has been models that fail to predict, even exacerbate, financial crashes as in the Long Term Capital Management fiasco of the 90's.
In Isaac Asimov's "Foundation" trilogy, the Psychohistorians try, over centuries, to usher the galaxy from barbarism into a second empire through the use of mathematics. Their calculations are based on the actions of quadrillions of humans but their plan is thrown off kilter by a single mutant, The Mule, whose influence was unaccounted for in their models. I'll try not to draw any modern day parallels here...
3
Yes very true, but when the Mule died things returned. We don't have a model nor data as assumed by Asimov. But yes the president should be as disruptive as that Mule, if he had those powers the disruption would be massive.
1
There is an assumption in some of the comments here that the United States has been and is now a pure Democracy where the majority vote wins in all instances. This is simply not true. The USA is not now and never has been a pure democracy. The country was designed as a republic with some democratic elements to it. It is now more democratic than it has ever been, but it is still a Republic, not a democracy.
The issue before the Founding Fathers was whether to have a constitutional monarchy, or a democratic Republic. The US Constitution itself was not really democratic since it required that three-fourths of the states adopt it before it would go into effect. The Electoral College was created specifically to avoid the result of a majority popular election and the original national electorate consisted of a small minority of white male property owners who choose electors to exercise the actual vote for the President of the United States.
Our whole history has been one of gradually expanding the electorate to include male African-Americans, Latins, Asians & eventually women of all races. We have also expanded the elected offices to include the U.S. Senate, which previously was appointed by the legislatures of the several states. Thus, we remain a Republic but the democratic elements of that Republic have expanded over time.
11
risk analysis which combines the probability of an event with its impact if it occurs is the best way to evaluate an event.
3
Those of you advocating for the interstate compact (in which states agree their electoral votes will go to the nationwide winner of the popular vote) are being just a little bit silly. The Republicans have a _massive_ advantage in the electoral collage because they are a majority in a large number of low population states; so no Republican state will agree to enter such a compact and risk diluting their influence.
They will also never allow the electoral college to be abolished. And (this is something I hadn't learned about until very recently) they will never allow the House of Representatives to grow so that it will become closer to the founders' notion of equal population states having proportional representation in the House of Representatives. (As the population grows in large population states, the number of representatives they have in the House is effectively capped because the total # of Reps can't increase; so proportionally the small population states are also greatly over-represented in the House.)
4
Good analysis, except if several states only have one congress person. Otherwise you are incorrect about that. Currently there are seven such states, there may be more in the future. Now of course those rural states are never going to give power to those over populated ones.
2
With any single event, the event will or will not happen. Two terminals: yes and no. That is the basic misunderstanding. Until the time for the event has passed either result is possible no matter how improbable it might seem. Only after the fact is a certainty possible. That is why one must plan for what the enemy can do and not just for what one thinks the enemy will do. A 5% casualty rate means 1 out of 20 will, over the long run, die.
There is no right or wrong about political faith, including political faith woven through numbers. It is fitting this is discussed in the opinion section. Instead of right versus wrong, the spectrum is defined by winning or losing. Please don't spin the two phenomena together.
Can all the talking heads PLEASE lay off the “Obama should have done more but assumed HRC would win” talk. Remember - Obama went to McConnell to ask if the GOP would support a stronger statement on Russian interference with the election (in Sep or Oct 2016), and McConnell said “N-O”. So just ask yourself - imagine how things might have gone if Obama had spoken up.
First, the GOP would have thrown a fit. Second, Trump would have used this to his advantage, and likely had a stronger win. Third, the Russian-FB-Twitter propaganda network would have just flooded the voters with fake news about this issue, leading to Obama leaving office in disgrace. Lastly, Trump would have been in a really good position to shutdown all inquiries into the Trump team and the Russians because of the “Obama political assault on the election”, meaning we would still have Trump but likely not Mueller and his team “digging for Chyna”. So please - knock it off. EVERYONE could have done a better job here - Obama and the Press included.
15
I believe he did a lot of things thinking Hillary would win, but perhaps not Russia. If he had gone to the senate on several things and also the dreamers he might have lost, but at least he would have been doing his job under the constitution, rather than not.
1
Mr. Leonhardt might follow this up with how statistics are handled in the Intergovernmental Panel on Climate Change's report. Also, who has read the report, especially the Summary for Policy Makers--and how important is it to act on the findings now, as opposed to 10 years from now (probably too late). Politically this means a key issue Democrats should be pushing is hardly even mentioned. This issue alone would increase turnout among first time voters, who traditionally have low voter turnout. The Democrats are letting the Republicans set the agenda on Climate Change, the same as on healthcare.
6
Democrats let the Republicans set the agenda on almost everything; this is my overarching complaint about my party.
6
Yes read the summary, it really tells you everything you need to know. Of course you don't know anything about measurement systems, or say physics so why bother with details that are clearly beyond your ability. Just do as you are told, that will work out well for you.
1
The do??? So why is the ACA still in existence, no infrastructure bill, etc. Now the media is easily distracted by shiny tweets, they should be reporting on Dem alternatives for our many problems, if they actually exist other than resistance.
1
One of my thoughts while reading about the reporting of probabilities in elections is that the news media in general has quite a bit of influence. I remember how, during the presidential election, the media gave free air time to Donald Trump because he was continually outrageous and seldom let go of Hillary Clinton's e-mail debacle despite her consistent message.
Left with the numbers, the probabilities were most likely skewed while there was much that just never got reported. I kept waiting for the real story to be told and I never heard it until after the election.
11
The New York Times contributed to Trump’s win (which, as we all know wasn’t a one person one vote win but a win dependant on constituency skew) by giving Trump’s antics more mention than he deserved. As a commentator from a distant land who never sees the print edition, I was dumbfounded by the number of Trump name mentions and how little was devoted to Hilary and her policies. By July, I was sure that he had it in the bag.
6
And you still have not heard it either, the press restricts facts and reports rumors and leaks. If there were evidence of "collusion" surely it would be public by now.
2
I disagree with the claim that probabilities are inherently hard to grasp. The examples given don't support the claim.
The intelligence officer's decision to risk war was aided by the estimate that the probability of war was only increased 10%. No doubt the officer could supply a story that justified a 10% increase in the risk of war as part of the job. Kahneman appears to have believed that supplying a probability estimate would more effectively influence decision making toward a desired result. I agree that many people share this misunderstanding, which is different than "hard to grasp."
It is risky to assume one knows the background information used in decision making. We can assume the intelligence officer had privileged access to secrets that, if known, would offset the disbelief that a 10% increase in the probability of war wasn't decisive on its own.
In the case of the Obama administration's response to the evidence of Russian interference, the assumption that the driving factor was an election result, rather than an interest in preserving the integrity of the election process as a core democratic institution, renders the probability involved moot. Perhaps the Obama administration was concerned to keep this crucial matter from becoming the political football it has since become.
That said, keep the Piketty-style inequality graphics coming. You are doing us a real service with them!
2
A study (unsure whose) also found that people will choose the sunnier scenario, even when faced with a really grim set of prospects. "30% chance of survival? Hey, I've got this thing beat!"
2
Lots of comments are about the problems created by the Electoral College system.
An interesting solution is growing in popularity and doesn't require changes to the Constitution. So it's actually feasible in the fairly short term.
This page describes it well. I encourage people to read it and if you like it and don't live in a state that has already signed on, contact your state representatives and advocate for it.
https://en.wikipedia.org/wiki/National_Popular_Vote_Interstate_Compact
2
The states formed the federal gov't.
States are still important.
The Electoral College process places states in their rightful place, and the sort of downgrade we see in dividing up a state's votes is destined to demean or diminish the status of the state. Why do what Venezuela does?
2
In 2 of the more recent Presidential elections, this change would've favored the Democratic candidate to the detriment of the Republican. In the future, the situation may be reversed. Would you be so in favor of "state's rights" as you apparently are now?
Also, you could also have said, "why be like Switzerland?" The meaning of the hypothetical comparison with Venezuela is obvious.
Venezuela? How about doing what every other democracy does: count the votes!
Why do citizens elect their senators but states elect the president? You say states still matter. How?
If you conceive, as the founders did, of the federal government as coordinator of states' actions, OK. But that's not how the federal government acts today, hasn't been since the 1930s at least.
The constitution has been amended to make our system more directly democratic. Senators are directly elected. The federal government can levy direct taxes. That the president is still elected by the electoral college is a remnant of the founders' original, untested conception of how the country would be governed, not the product of 200 years' experience.
The national popular vote pact is a practical route toward further democratization. It would give a voice to the voters in the 38 non-battleground states. It can't be ratified too soon.
1
You don't really say what you got wrong. You COULD if you worked out the odds that the odds you worked out were right. That is, for the set of all events of which you gave each one a 50-50 chance of happening , were you right half the time? For those that you gave a 2 out of 3 chance of happening, were you right 2 out of 3 times? That's the best way to determine whether the prior odds you offered were borne out -- whether you were a good bookmaker.
4
Love this. Best book (OK, most useful book) I ever read was Huff's "How to Lie With Statistics - should be required reading for everyone graduating high school in the USA. One correction to your conclusion, though: Electorally, we do get to "try again" - in 2018 and 2020 and.... Hope springs eternal, even in dystopia.
2
I made a good part of my income playing poker, and if one fails to understand that being a 10-1 favorite means you will lose one out of eleven times, you will go broke.
5
Is it that people need stories or an education, including probability as a K-12 staple course?
1
The unpleasant truth is that today's white non-college educated working class person is not your grandfather's white non-college educated working class person.
Eighty years ago, there were many very intelligent people who did not attend college because of financial circumstances or because of discrimination against their race, religion or gender. Henry George, arguably the most brilliant American economist of the 19th century, left school at age 14. President Harry Truman was not a college graduate.
Today, with many exceptions, someone under the age of forty who was never interested in college probably is not very smart. That could reduce their wages. That also makes them vulnerable to the lies that got Trump elected. Even some with college educations are not able to understand that NAFTA and trade agreements in general increase employment and standards of living and that immigrants are not responsible for slow economic growth. ..."
https://seekingalpha.com/article/4133734
1
So Trump ACCIDENTALLY won in a LANDSLIDE? 57% to 43%. Very interesting.
3
You are ignoring the actual votes cast by individual voters. Trump did not win a majority of those votes. The Electoral College introduces a whole other level of complexity into calculating probability of winning a presidential election. So does partisan gerrymandering and the many methods of voter suppression, such as fewer voting machines per capita in certain precincts. You are correct in saying that Trump was not elected by accident. Gerrymandering and voter suppression laws enacted by GOP controlled state legislatures were not an accident, and Trump benefited from them.
2
He lost the popular vote by 3 million which, historically speaking, is considered a large margin. We don't use the word "landslide" with the electoral college.
2
Sure we do, not that Trump did that. But if say a president won every state except say the west coast, new york, and some other small liberal states that would be a land slide.
2
It seems the problems is not probabilities, which are the best way of expressing the likelihood of anything happening. The problem is with poor thought process among leaders.
3
Accurate estimation of probabilities is also a very big problem. By definition, we know with a high degree of certainty the probability of a head or tail from a fair coin, but elections and international relations are not fair coins. The more imperfect the information you have, the more imperfect the conclusions you draw about the real world. Giving decision-makers guesses is better than giving them nothing, but only if the decision-makers understand not only what your guesses mean, but also the degree of uncertainty behind those guesses.
2
Any system that gets us a Trump win gives no protection to the citizens of a democracy. Could there be worse demogogues ahead ? Yikes.
Here's what's undiscussed in our media: Do other world democracies have an electoral college system to try to balance their bigger/smaller states or political regions? Why not?
Pew Research: “Among democracies, U.S. stands out in how it chooses its head of state.”
Washington Post. The Fix
“How do other countries elect presidents without an electoral college? Pretty easily. By David Weigel December 20, 2016
Says--- “There are 4 years before this will matter again, and there's absolutely no hint that it will change. But it might be telling that when we've advised a country on how to write a constitution, we have never told them to copy the electoral college. Nor have we told them to let state legislators draw their own boundaries.
In 2012 our system elected a House of Representatives that lost the popular vote and in 2016 it elected a president that lost it, too. That has massive distorting effects on how our country works. For all our gifts, it's something no other presidential democracy has to worry about.”
So, David Leonhardt might write a compare/contrast column instead of this statistical probability gobbledygook. Get input of Drs Kahneman and Welch on how our election system affects voter psychology, and either supports or detracts from democracy.
4
Meredith, your rant against the electoral college is somewhat misguided. Not that I think keeping the EC at this point makes a lot of sense as the EC disenfranchises all voters in heavily red or blue states.
But, you can't assume that HRC would have won the popular vote IF the election had been run under the rule that the winner of the popular vote is the winner. If that had been the case, two things would have happened for almost a certainty: 1) both campaigns would have changed their strategies and gone after votes in every state if every vote counted. Trump hardly campaigned in NY, and I don't believe he went to CA; 2) voter behavior would change in heavily red or blue states. For example, in CT it is a foregone conclusion that the state will vote democrat for Pres so there is little motivation for either Repubs or dems to vote in the presidential race. BUT -- change things so the popular vote determines the winner and it is a completely different ball game for voters.
3
What is needed is proportional representation; an electoral system where the divisions in the electorate are represented proportionately in the elected body as other countries use.
1
I adore the cheerful, right-wing Trump echoing know-nothingisme in that "almost a certainty," and would simply have adored seeing Hizzoner on the stump in the most populous states.
This is a really helpful explanation of why to take low probabilities seriously. Thank you.
2
Why, when it comes to lottery tickets, do people not round the odds down to zero?
4
Buying a single lottery tickets increases one's odds of winning by an infinite amount!
Maybe I'm missing something; the title of the piece is "What I Was Wrong About This Year," but goes on to state how and why others have been wrong about this or that. Where's the "I?"
10
One of many vulnerable voices leaves no need for "I" in particular.
1
He says he was wrong about thinking people understood probability.
1
What you were wrong about was not recognizing that the American democracy has been destroyed by unlimited anonymous contributions to candidates for public office.
9
And a system vulnerable to computerized electronic vote manipulation. With private companies running the process the era of casino gaming-style election results is all but assured.
How Hackers Broke Into U.S. Voting Machines ...
http://fortune.com/2017/07/31/defcon-hackers-us-voting-machines
The Insecurity of America's Old and Underfunded Voting Systems
http://www.npr.org/programs/fresh-air/2017/07/20/538312289/fresh-air-for...
https://harpers.org/archive/2012/11/how-to-rig-an-election
There is no evidence that this actually happened, it could but did not.
1
You weren't the only one that got the 2016 election predictions "wrong". Basically all the mainstream media pundits and statisticians came up with the same result.
When all of you do, then it's not we and our lack of statistical knowledge who are to blame.
You guys simply used the wrong data set.
GIGO
Garbage In Garbage Out
Predictions based on nationwide voters' preferences are meaningless when we have an electoral college system in which low population states have an outsized influence.
Had polling been conducted more carefully, STATE BY STATE, factoring in the way the relationship between the electoral college and the popular vote, you might have gotten it right.
Mr. Leonhardt, it's okay to admit you are wrong. The problem wasn't us, the readers, who trusted your expertise. It was you and your colleagues.
5
Pundits may have gotten the results wrong, but many statisticians did not. As David points out, saying that Hillary had an 80% chance of winning does not mean they are wrong if she lost. Here's an example. The chances of rolling a seven on a pair of dice are six out of thirty-six, or one out of six. That means the probability of not rolling a seven is just over 83%. If you do roll a seven, it doesn't mean the statisticians are wrong. It means people who read 83% as a sure thing were wrong.
6
"Saying that Hillary had an 80% chance of winning does not mean they are wrong if she lost."
True, and I totally understand that. But just because they SAY she has an 80% chance of winning and calling themselves "statisticians" does not necessarily make them right either.
I am questioning the basis on which they built their probability. GIGO
Did they start with garbage?
It looks to me like that is a distinct possibility, and one which Leonhardt carefully avoids addressing in his article.
2
Not only that since many did exactly what you describe. Some voters won't tell you the truth, your sample might not be representative of those who actually vote. I know for say internet surveys I don't always tell the truth. Not to mention that people change their minds, weather can influence who turns out and many other variables that are difficult to predict.
1
If the Trump administration decides to attack North Korea the probability of hundreds of thousands of deaths in South Korea is 100%. I don't have enough data to offer a probability of millions of deaths on the probability of millions of deaths.
2
I think there's about a .3% chance that this column will make a difference.
6
As I learned in a "stats & probability" class a long time ago:
1. An occurrence whose probability is not zero is possible.
2. A winning long shot always brings down the house.
2
It's hard to get people to take probabilities seriously. As Leonhardt says, they want a story. They round up to one, or down to zero.
It's an ingrained trait in most humans. Binary thinking is simple and often useful when quick decisions are required, and it probably have deep evolutionary roots. ("Will it eat me, or can I eat it?")
But, living as we do in a world of symbolic threats, it's dangerous. We need to move from measurement on a nominal scale (EITHER/OR) to an ordinal scale (MORE OR LESS). It's not that big a step but it requires effort and a loss of certainty.
To begin with, we need to pay attention to those nettlesome levels of confidence ("plus or minus three percent") that accompany every poll. The widely accepted level of confirmation in science is one chance in twenty that your guess is wrong. One chance in one hundred is even stronger evidence that you're right.
And we need to remember that probability never achieves unity. "Will the sun rise tomorrow?" The only correct answer is "probably."
1
I failed, as did other observers here, to read just what errors there were that David Leonhardt admitted to. What I DO read in many of the comments is more blame on the "antiquated Electoral College" and more clamoring for direct popular vote national elections. What I fail to see are concrete suggestions for doing away with the EC, or at least make its voting more representative.
For years I have suggested getting rid of "winner-take-all" voting in ALL states (Nebraska and Maine did so years ago and the sky did not fall). I vote in NY, one of the 48 winner-take-all states and do not see how such a system is in any way fair or representative. In a hypothetical 50.1/49.9 split in the popular vote for a national candidate, the 49.9 might as well have stayed home, their votes are discounted to zero and the "winner" gets all the electoral votes. Proportional voting is far more rational, whereby each candidate gets the number of electoral votes according to his/her percentage of the popular vote. The EC gets to vote as usual, but with a much more accurate representation of the wills of the voters. My Republican friends (admittedly few) claim that "it's too confusing that way." Partial votes can be rounded up or down. Or as Solomon decided, people could be cut in half. It's not rocket science, it's arithmetic.
8
Jeff, you write, "What I fail to see are concrete suggestions..."
Actually, there is an idea out there this is a very concrete and interesting suggestion and some states, including California and New York, have already acted on it. It's called the National Popular Vote Interstate Compact. I encourage you to read about it in the link below. In short, states that agree to the compact agree to assign their electoral college votes to whichever candidate wins the majority of the NATIONWIDE popular vote. It is not necessary for every state to agree to the compact for the system to work. Once a critical mass of states agree, the compact will go into effect and the nationwide majority winner will be awarded a majority of electoral college votes. The advantage of this approach is that it does not require any changes to the US Constitution.
https://en.wikipedia.org/wiki/National_Popular_Vote_Interstate_Compact
2
Just want to recommend two books.
Innumeracy by John Allen Paulos
The Signal and the Noise by Nate Silver
3
The only certain number for outcomes is 100%. Anything below that, the coutcome is a probability.
David, You realize, of course, that you have just made a compelling argument that more people should be required to have a more extensive and better math education. If probability is to play an ever increasing role in modern life, then people need to intuitively understand what probability implies, and not have it explained to them for every context in which it appears.
6
I agree completely. Except that this is statistics, which at least in my day wasn’t taught in high school. I know scientists with PhD’s who don’t know basic statistics.
1
One of the biggest mistakes most folks make is called the Ecological Fallacy - consider the following:
if the average score of a group is larger than 100, it does not automatically mean that a random individual of that group is more likely to have a score greater than a 100 than one less than a 100.
How many times have each of us committed this fallacy?
2
Law of averages David. Your probabilities can be wrong. That's no big deal. When every statistician is wrong though, people get upset. That's not a communication problem. We're not talking about discrete probabilities. 2016 is outside the standard deviation of a normal distribution. Everyone shouldn't have gotten 2016 as wrong as they did. You math types were way off. That's the difference. You don't need to understand statistics to understand the error.
1
If a 200 hitter in baseball gets a hit, does that mean the statisticians are wrong? Once again, the fact that a less likely event occurred does not mean the the math types were wrong.
2
Andy of Salt Lake City, Utah, writes: "Law of averages David. Your probabilities can be wrong. That's no big deal. When every statistician is wrong though, people get upset. That's not a communication problem. We're not talking about discrete probabilities. 2016 is outside the standard deviation of a normal distribution. Everyone shouldn't have gotten 2016 as wrong as they did. You math types were way off. That's the difference. You don't need to understand statistics to understand the error."
There is about a 68% chance that the prediction will be within one standard deviation of the mean. I wouldn't call being outside that wrong! It's probability. Sometimes the longshot wins. Now, if the longshot wins too often, that's a sign of problem. But you can't say any single prediction is wrong. You need better "statistics" than that!
1
Well put.
The biggest mistake that pundits make is that they accept no responsibility for the results of their pronouncements. Predicting that Hillary would win, many potential votes for her stayed home. We got Trump instead. You, Mr. Leonhardt, and those with a similar pulpit, are partly to blame.
Be careful what you say. People actually listen to you.
2
Probability of one occurrence, instead of another, given existing conditions, all of which should be known, or a tremendous effort be made to know existing conditions, if one doubts one has collected enough data, from all available sources, sources meaning real in your face solicitation of data, instead of second hand information and opinions.
So, presuming the forgoing had occurred, in the 6 months leading to the Presidential election, and presuming the modern-day Boss Tweed (Hillary) and the modern-day Tammany Hall (DNC), had not engaged in their deeply hidden agenda, and the in-your-face corruption, and the carefully thought-out and executed sabotage of the Bernie Sanders campaign, our 45th President would be Mr. Bernie Sanders, the gentleman, in every sense, from Vermont, and the entire Trump nightmare would never had occurred.
I liken published probabilities, in mainstream media, to a concerted effort to manage perception, on a massive scale.
Huh?! The future by definition is unknowable. Therefore, any prediction of events can never be judged "wrong." The only error then is made by the human choosing to make a certain conclusion that turns out to not happen--and then blaming the prediction.
2
I am amused at David Leonhardt's argument, or the arguments of the readers. A year's high school course in American history seems to have been left out to chase the fantasy of probability. At my school much of that year was spent studying the American Revolution, the writings of the Founders, and the American Constitution. And, quite specifically, why we elect the President through the Electoral College: The Founders believing that, given a 1790s population of uncertain literacy and political experience, a buffoon or potential dictator might seduce the public into awarding him the powers of the Presidency. The could be prevented by interposing an Electoral College composed of more experienced statesmen with the courage to deny the "popular will" and interpose their wisdom.
In this election the polls were quite right, Hillary had the popular vote. In fact, she had a substantial majority. She would have been easily elected President by most state laws for electing Governor. And, one might have presumed the Electoral College would understand its duty and give considerable thought to the danger of electing a buffoon. They did not. Instead, they rigidly cast their Electoral College vote exactly by the rules, showing the utter folly of the Founders in believing the "statesmen" following them two centuries later would understand and follow their wisdom.
21
"The Founders believing that, given a 1790s population of uncertain literacy and political experience, a buffoon or potential dictator might seduce the public into awarding him the powers of the Presidency. The could be prevented by interposing an Electoral College composed of more experienced statesmen with the courage to deny the "popular will" and interpose their wisdom."
Best argument for reconsideration / reform of the electoral college, which in its righteous adherence to the well intentioned founders, instead provided us with the buffoon.
3
I wish we could hold the E.C. voters accountable for criminal malfeasance. However, what is needed is proportional representation; an electoral system where the divisions in the electorate are represented proportionately in the elected body as other "enlightened democratic" countries use.
1
Your biggest error was to believe that their are significant non-tax causes of inequality today.
"..Conventional analysis of the impact of tax legislation on inequality makes a profound error. Many use the terms pretax inequality and after-tax inequality. This terminology misses the causal relationship. A hundred years ago, looking at pretax inequality and then estimating how much the tax code impacts inequality might have been logical. That assumes there are some significant nontax factors that are causing inequality and tax law can then increase or decrease the degree of inequality. There is at any given point in time a degree of pretax inequality. However, almost all of the variability of pretax inequality since at least World War I has been the cumulative effect of tax and other legislation.
Prior to enactment of the Federal income tax in 1913, all inequality was due essentially to nontax factors. The first Federal income tax in 1913 reduced inequality, since it was a tax of 7% of income above $500,000. At that time $3 a day was considered a good wage. Thus, originally only a minute fraction of the richest 1% paid all of the Federal income tax in 1913.
Obviously, wealth inequality, which is a function of cumulative prior income inequality, does cause income inequality. However, other than wealth inequality, there have not been any significant nontax causes of income inequality for at least the last 50 years..."
https://seekingalpha.com/article/4133734
2
Priorities for the Democratic National Committee and All Democratic Party Officials
Job #1 should be to establish and maintain integrity.
Job #2 should be to engage the best available cyber security for communications and web sites.
Job #3 should be to understand the differences between Progressive world views and Conservative world views
Job #4 should be to explain the Democratic messages simply and clearly using the best behavioral science.
Job #5 should be to do proper vetting and due diligence on all candidates, nominees, platform positions, and proposed actions to avoid public embarrassment of the party and its leadership.
Job #6 should be to get proper identification for all persons eligible to vote registered.
Job #7 should be to get all persons eligible to vote registered.
Job #8 should be to get all registered voters to actually vote.
Make sure that your Democratic Party walks the talk.
No fake news.
No exaggerations.
No cute deceptions.
No cheap shots.
No gloating over Republican circular firing squads.
No heckling.
Explanations rather than attacks.
Seek first to comprehend.
20
Jobs 7 and 8 need to be jobs 1 and 2, especially since in many red states registration and staying registered is no easy task and mail-In voting is not permitted.
Registering voters and getting them to polling places require months of proper planning mobilizing many, many volunteers, and adequate funding. If qualified voters are prevented from voting or don't show up to vote, the party can have the best ideas in the world, but it still will not prevail. For 2018 and 2020, all of us who oppose what is happening need to get down in the trenches not keep our heads in the clouds.
8
The three most important things that the Democrats should focus on are:
1. Prevent the Russians from rigging future elections.
2. Prevent the Russians from rigging future elections.
3. Prevent the Russians from rigging future elections.
The Russians and the Trump wing of the Republican Party are continuing to learn what to do and what not to do in future elections. They will be much more circumspect and take greater efforts to conceal their activity next time. Much more emphasis will be on rigging the voting machines.
If Democrats take over Congress in 2018, they will have an independent commission to study Russian election rigging and develop ways to prevent it in the future. If the Republicans maintain control in 2018, Russians and the Trump wing of the Republican Party will be able to employ much more sophisticated methods to rig future elections..."
see: http://seekingalpha.com/article/4034048
If the Russians are not able to rig the 2018 congr
2
If humans need a story, learn about what Heisenberg's uncertainty principle really means.
I'm reminded of a statistic I heard one time, where the analyst concluded that the people in Minneapolis were as fit as the people in Honolulu, based on gym memberships per thousand people.
What's wrong with this story? The people in Honolulu exercise outdoors. If gym memberships are a tie, Honolulu wins.
The analysis of this election missed two important factors: the Democrats were doing a lousy job, and people don't like Hillary.
First, the Democrats: I know they faced massive resistance from the Republicans, but still, what they offered was not good enough for working people. Americans need an environment where being an ordinary person of ordinary means, who is willing to contribute, leads to a reasonable lifestyle. The Democrats didn't offer a solution. And Obama wimped out when the chips were down; he should have asked the Supreme Court to rule on whether he had the right to nominate the next justice, instead of letting the Senate steal his seat without putting up a fight.
On to Hillary: She never faced down her opponents and stated clearly "I was the boss at the State Department, and I made the rules there. The email policy is what I said it was." Instead, she waffled, weaseled, and still won the popular vote, but she was outplayed in the midwest by someone who understood the elector college better that she did.
I have a quote from Dr. Zhivago for the Democrats in the future. "Adapt yourself." The people need more than you have been offering.
6
Here's hoping Trump's wish that all Americans celebrate a Merry and White Christmas never comes to pass. Happy Saturnalia!
1
The column's title is "What I Was Wrong About This Year", yet it didn't contain even one example of what the columnist was wrong about.
Very disappointing, and misleading.
8
Edward Tufte has some excellent books on the graphical representation of numbers and ideas. Worthwhile reading if you are someone who has to explain (or understand) abstractions.
1
Pseudo science David. Pseudo science. It may be useful to sell newspapers and this piece makes an amusing read, but there is absolutely NO WAY that probability theory can be used honestly in predicting political outcomes. Rather than apologising for getting it wrong, and then getting into a ridiculous explanation that your readers just didn’t understand commonsense, you should be apologising for your use of pseudo science. False news, David. The Israeli story is a good one though, because it demonstrates how unscrupulous advisors can manipulate politicians by dressing up their schemes in an apparently scientific manner. Makes me wonder whether George W’s advisors sold him on the weapons of mass destruction fiasco using the same technique. Smoke and mirrors, David. Illusion. Probability theory has valid use in medicine (providing there is accurate data) and also in trend analysis for companies such as Google or Amazon having mega data and mega computing power. Weather forecasting, physics, astronomy Yes, politics at both a national and international level, No. As for those commentators who have built on your illusion by suggesting modifications to the method, they deserve to be put in a sack with Schrödinger’s cat and dropped in a creek. What do you think of the probability of their survival?
4
Hillary lost because people did not come out and vote. They didn’t like her and they ceded their civic responsibility to everyone else. Let’s see if they’ve learned their lesson in November or if they are swayed by the pennies they get in their tax cut while the wealthy rob us blind
8
Yea of little faith. Facts, evidence-based knowledge, honesty and personal integrity are and remain the winners here. They endure and have a proven track record, outlasting reckless prezident trump. Stay the course and bask in the renewal it has brought, especially in this season of Christmas and Hanukkah.
So we round down to zero. Because have bias. In the Israeli case...few wanted war with Syria, and 10% looks to us non-mathematicians as low. If I have a 10% chance of getting a new job, but have to jump thru hoops to just get an interview...I wont bother. Raise that number x 5...and I reconsider.
We, individuals, judge these things on our own internal, albeit faulty, "whats in it for me" calculator. What does it cost me? What do I gain? If one, the costs, outweigh the gains (both perceptions, not necessarily real) I will tend not to take the risk.
Actually, the polls were correct. Hillary won a majority of the popular vote, and by a number larger than any other candidate in history besides Obama. The Electoral College turned out to be the proverbial “thumb on the scale,” that enabled the manipulation of the election by nefarious forces, be they Russians or someone else. The election was rigged by our own laws that were designed to prevent exactly what happened. Advocate that your state change its laws to grant electoral college votes based on the winner of the popular vote. We no longer live in a world where ignorant people in the hinterlands need smarter heads to make their decisions for them, or where smarter heads need be overruled by those who insist on the superiority of their ignorance. Some 63 million people who voted for a shameless demagogue were permitted to force their hideous views of the world on the rest of us. This should never be allowed to happen again. Vote in numbers that befit the oldest democracy in the world. Take back the republic from those who have stolen it. Vote in 2018 to remove this administration’s perceived mandate and its power to destroy our country. What we’ve seen this past year is not who we are or who we aspire to be. America doesn’t have to be like this. Selfish, brutish, nasty, petty, and cruel. VOTE.
9
".......the oldest democracy in the world". The Alething, the National Parliament of Iceland was founded in 930 AD.
The fact is that how many mistakes you've made is irrelevant to me. You dispense opinions for the masses and what you said yesterday has little importance today. Sometimes your opinions make sense, sometimes not. I would care a lot more if you held real political power.
1
and then there's the electoral college....the polls were roght.She got the vote.
True, True, True. And we have the electoral college, the very antithesis of our esteemed Democracy of which we are proud being the womb etc. etc. Even Iran our Pariah, has a better one! The electoral college is our version of Putin.
The real problem is that no one foresaw the way probability/statistics and more specifically regression equations and big data would be used to elect another wildly incompetent Repug to office while winning a minority of the votes. It is called "Redmap."
The majority of Americans knew who would be the better president, for the second time in a few years. You can alway persuade a minority to go with a fool, or an authoritarian, or a dictator, or some one as bad as Bone Spur.
Democracy, the wisdom of the majority and the overall social system in this country has a will work fine.
Putting minority candidates into office is a bi-partisan problem. Those fine Republican folks in the country will be justfiably as offended and the damage to the country will be just as negative if it were Dems that were putting non-majority candidates into office. Bone Spur is an embarrassment, but there actually even more problematic candidates out there: Try Ted Corrupt Cruze.
So, Wake up folks - Dems, Repubs & Indeies . The problem is the electoral college and how some real smart computer programmer figured out how to use statistical prediction and big data to undermine democracy.
1
Many many years ago when my computer hung off my belt and was made of some fine wood our professors drummed into our heads that probability must be associated with a measure of consequence.
So a scratch-off NYS lotto ticket that "promises" a 10% chance of winning $10 is worth a shot at $1.
But not at a cost of $1.10.
Or if that $1 plays into the probability that if you buy a ticket you'll have a 90% chance of not being home in time to meet the kids (say a bus fare is $1.50 and you only have $1.50 in your pocket) then you'd be insane to risk it - seeing as your wife acting like you don't exist for a week would be VERY painful environment.
Or if a 10% chance of causing a war associates with 1000s killed and billions of $ needlessly wasted ........ wellllllllllll ....... you get the drift!
1
I'd absolutely agree with our refusal to understand basic stats--but I'd also point out that the Times' "Upshot," section DID publish lists of "paths to victory," for Donald Trump, and charts showing cascades of paths to winning.
Posters have been screaming at Upshot for over a year now, even after being given a ton of tools (see the "as likely as a NFL kicker missing a field goal from -----yards"). They didn't care.
My suspicion is that they'd already settled on a story (the media lies because it hates Trump! The media lies because it hates Sanders! The media lies because them egghead liberals hate workng stiffs! The media lies because them egghead liberals is just smarty-pantses!), and won't let go, whether it's a triumphant slogan or an alibi for loss.
1
What I was wrong about this year:
Well, it took me about 15 minutes to fully understand that Trump is a fool, a knave and a bozo capable of ruining this country. A tragic mistake on my part, because I had just been about to embark on a massive fundraising campaign on behalf of Alfred E. Neuman, a man of intelligence, impeccable character and humor who would have mopped the floor with Trump and made a fine President.
Mr. “What, me worry?” vs. Mr. “I’ll make you worry.” Ah, what a loss!
http://www.madmagazine.com/tags/alfred-e-neuman-for-president
3
What's the probability of Trump being elected president in 2016? What did you say?...I didn't hear you!
1
What were the probabilities that Hilliary supporters and the media would be in identity shock that the Donald would be President of the United States?
I like 100%, Alex and I will take Fake News for a $500.
I giggle every time I think of the realization that made Judy Woodruff's mouth and face droop on election night as the future was slowly unveiled to her on live television.
I like a message for the Dims: “ Don't believe everything you think .”
What are the probabilities for 2018 being as good as 2017 ?
1
Great David thanks but what DID you get wrong this year. You left that out. It was the title of your post today
2
"Oh Jeez!" as Archie Bunker would say. This is the NYTimes and David Leonhardt trying to justify the NYTimes daily running prediction of assured Clinton victory. Just because the dice might NOT fall the way they are expected to, by editors and readers, is no reason , like the isreali army guy-to read whatever results into the numbers they want.
The NYTimes front page was still extremely sure that Mrs Clinton would win because it devoted almost all it's attention to Clinton and what she was planning to do after the election, who she was planning to keep and who was being fired. (Trump was convinced)
After the election, after the dead silence of terror among the Democrats. As realization sank in among the people who claimed membership, but voted communist or green or tore up ballots by voting for Sanders, the
panicked telephone calls began and the explanations and excuses-like Leonhardts-began. I received a call from a Democratic fund collector explaining why I needed to give immediately-even though she had been one of the members of the party who voted for Sanders"But we know better now! The NY Times SAID she was going to win! We were angry at her for spending time with her Wall St. Pals!"
Like Leonhardt and the Times, too many Democrats don't understand how our electoral system works and so we may have 8 years and a blow up before another Democrat is elected. This is not Big data-its small: Vote ONLY for your party's candidate. Never expect others to do it for you.
4
Sometimes the word "rare" does the trick. Or simply putting the odds in a positive construction. In the case of disease, a person may have a 1% chance of contracting a specific illness, so rounding to 0 is a huge temptation. Saying that it is rare, or that one person in 100 will get the disease may transmit the fact that the disease does happen to people, and I have a real change of getting it.
The over 50% and under 50% look like positive and negative rather that two positive realities (the odds that the even WILL happen).
On the other hand, people in the business of predicting things like electoral outcomes should have done way better on the Trump/Clinton election.
1
I think the Times still has Clinton's chance of winning at about 65%.
2
So what you got wrong is you overestimated our abilities? That was your shameful error?
3
I think you(columnist) need a refresher on stats course. Pronto.
2
You were wrong to have stuck up for giving an honorable platform for the racism of the odious Charles Murray. This emboldened the pepes, and the trump enablers like bruni. It also confirms the gimlet eye with which we blacks look at people like you.
1
missed what you were wrong about.
3
Improve how people understand stats? How about *not trying to predict the future*!? When the NY Times or any other paper / site has a time machine with reporters constantly arriving back from tomorrow, _then_ I'll want to hear predictions about who will win, or what movies will be out of style, or what politician will announce what on Tuesday.
Sooooo sick of this kind of "reporting." I suppose it can't be skipped completely — not 100% avoidable, hahaha — but a little devotion to reporting on things that have actually happened would sure enhance credibility and avoid epic fails like the one last November. Not to mention making statistical conundrums like this a moot point.
End transmission.
2
Probabilities for one-off events (e.g., the 2016 election) are meaningless.
The real analytical question going into 2016 was "were African-Americans going to the polls at the same levels as in the recent past?" But this question would have raised the uncomfortable issue (for the New York Times) of the extent to which the Obama administration politically failed the core constituents of the Democratic Party (especially African-Americans). The New York Times is key in holding up the false narrative that the Democrats faithfully represent the social justice left -- which it doesn't. (The New York Times kept pushing this farce even after the Hillary Clinton [ill-timed] speeches to Goldman Sachs came fully into public view.)
8
It's all relative. The Democrats in Canada would be consider a moderate right of center Party akin to our Conservative Party whereas the GOP in Canada might well be considered a hate group and banned.
It's all relative.
1
What you need to do is to place the risk/probability combination in a simple 2 by 2 matrix. You can generally ignore the consequences of outcomes in the lower left, be greatly concerned about the outcomes in the upper right, and depending on your risk tolerance, worry about those in the other two quadrants.
High risk | High risk
Low probabilitv | High probability
_________________|_____________
Low risk |Low risk
Low probability | High probability
1
Appreciate the stats and here's another - there are only two chances in thirteen that an article by a New York Times Opinion Columnist will be written by a woman. Don't get me wrong, I love the NYT but shouldn't a newspaper that reports regularly on inequality in the workplace actually promote equality in the workplace? I guess if the stick figures actually have sticks (figuratively speaking) they have a better chance of getting their voices heard?
6
Well, maybe I'm a pessimist, but I wouldn't blow off a 10% risk of an adverse affect. If the weatherman told me there was a 10% chance of rain, and I really didn't want to get wet, I'd pack an umbrella on those numbers. Scout motto "Always Prepared!" If for some reason, hypothetically, I couldn't pack an umbrella, and I really couldn't get wet, I'd be getting more info on the weatherman. I guess this is the story. But, if the weatherman said, you have a 90% chance of staying dry, I'm not sure I'd worry so much about the 10% chance of rain, unless I really had to stay dry, not matter what. In our past election ---- a well known figure like Hillary Clinton, the first female with a real shot at the presidency, should have been highly concerned with a 72/85 percent chance of winning. It's upset territory for a first and supposed champion. People kept misdiagnosing her problems, prescribing the wrong medicine. They said she lost against Obama because she came out to fierce, so in her second go around when the place is falling apart and we are looking for this "Firework", she's "measured"? Sometimes I wonder if her team wasn't working for the other side. Crazy.
3
I was wrong about this column. The title made me hopeful that it might be a rare expression of humility from a NYT columnist. But no, it is more arrogant condescension. Yawn.
4
You’re correct that people need stories. What we needed before the election was not statistics about whether this or that candidate would win, but what would likely happen if he or she did, based on campaign promises and past behavior. Perhaps if people had seen scenarios of what we are now experiencing, millions who could make a difference would not have stayed home. Millions who voted one way might have voted another. Simple scenarios like “if x does y, z will likely happen.” If x gives tacit support to white supremacists, they’ll be encouraged to riot and cause harm. If x threatens the leader of North Korea, we will see the doomsday clock push closer to midnight. Based on past behavior, x is likely to cause great harm to the press. X is likely to enact policies that favor himself and wealthy donors and cronies than the people. X is a misogynist, so will likely avoid appointments of women to his cabinet. X is racist. See X is a misogynist. X is xenophobic. See X is racist. X is an unrepentant liar. See all of the above. Journalists are storytellers. Use your imaginations to help the people understand that elections have consequence, and what those consequences are likely to be.
It’s not as if we haven’t seen this before. All those “good Germans” claimed they didn’t know what was happening. But Hitler was clear about his ambitions. We have hindsight about what authoritarian leaders are likely to do. Make it clear so people understand. Numbers are abstract. Make it real.
1
An honest breakdown of this pundits short coming happens to be the same shortcoming of the NY Times and major America media outlets.
It is the UNINTERUPTED submission to sectarian issues while ignoring American interests.
No where is this visible as it is in the Palestinian Israeli conflict in which the USA played what could be mercifully called an absentee role , ignored basic long term American interests and declared an open war on the Arabs and Moslems!
It started with the absurd Self contradictory appointment of Jewish conservative majority in the representation of the USA in the said conflict foregoing the basic, elementary rule of a neutral third party in, this crucial Arab Moslem /Jewish conflict.
How more stupid can one be ?
It ended with the equally idiotic , timing wise at least, of a USA recognition of Jerusalem as the Capital of Israel......all that took place while the USA was finalizing its proposal for a peaceful settlement of the major ME conflict!
How more idiotic can one be ?
The Titanic sank and it was absolutely preventable. Greedy corporate managers ordered her through glacier ridden waters at a high rate of speed. Her interior structure did not prevent the hold from flooding. Emergency procedures were inadequate
To rescue those who should have survived.
Deep ambivalence is so out of place right now. Donald is destructive. His team is destructive. You do not have to be a Columbia professor to see the obvious: two thirds of us want him and his whole administration out. We simply lack the internal structure to secure our own safety.
If we were British an election would be called and an administration run by a mad hatter would be gone. But then again it is a mathematical/statistical certainty we are not.
For an increasing number of us all of the celebrating on our side of the street just looks to Donald and his boys like we are weak and vacillating. Maybe they are right. After all, he and his pals just screwed America’s middle class out of $1.5 trillion and they did not say a word. 2018 is coming—it will be too late for Bears Ears—I hope it is not too late for us.
6
..."lies, damn lies and statistics"
2
Statistics are a great tool, but most people do not know how to use them and quite often stats are applied to situations that do not have any meaningful correlations. Because people are terrible at judging stats and also terrible at judging the good from the bad, stats are used as propaganda. They are used to sell toothpaste and influence elections.
Humans have been weighing the odds forever. Should I risk everything to hunt an elephant and feed my family for the next full season, or should I just keep picking these damned berries and seeds day by day by day. Natural selection will sort those who are good with stats from those who are bad in the long run. And that is perhaps the pivotal part of this discussion. In the long run. Global warming is here. It IS the long run. But nobody would have noticed if we did not collect data and use statistics. The deniers do not understand data collection or statistics. They probably tailgate and are surprised when they get lung cancer after a lifetime of smoking. Natural selection will do its magic. In the long run.
Also... Somebody is eventually going to win the Mega-Lottery. The odds are staggeringly high that it will happen. In fact, it always does happen. In a related inverse matter, the odds are extremely low that YOU will win the Mega-Lottery.
Oh yes. Mr. Leonhardt. I am still annoyed with you for your blind support of HRC and total lack of interest in Sanders. Was that in any way the result of statistics?
3
Statistics and damn statistics . You can extrapolate anything you want. No more for me after the 538 debacle ( and all polls) of Clinton versus Trump. The NYT interactive map of how the 2016 presedential election might turn out did not even have Michigan in play! It was solid for Clinton . Ha Ha . Now look at the manure mess we are in . It is all horsepoop as they say.
Vote Vote Vote, act , act , act.
4
The problem in statistics is the Reality of the Schroedinger’s cat conundrum. No one gives a crap until you open the box and the puzzle collapses to one answer. If you predicted it incorrectly, you receive scorn. If you predicted it correctly, you may receive blame. Being a statistician must be an intrinsically frustrating occupation. On the other hands, it beats divining the future by reading chicken entrails, which don’t appear to be readily available regardless.
1
One of the election-news sites I was following in 2016 had a banner showing the probability of a Hillary Clinton victory, which usually hovered at or about 75%. To prevent complacency-inducement, it accompanied this with some text saying "this is about the odds of an NFL kicker making an x-yard field goal" ("x" varying with the probability du jour). As a generally sports-averse person I'd have preferred a different type of example, but I got the point: close-in field goals are not infrequently missed; even extra-point kicks are. Sports-averse I am, but never worry-averse, and this gave me plenty to worry about.
I think this may be a good way to relate cold-number probabilities to real-life situations in a way that people can feel.
1
I was always heartened when the doctors deemed that there was only a 1% chance that my son would be afflicted with what my son has. For us it was 100%.!
What? I was told that Clinton got more votes than Trump.
Ah, y'all must be talking about that strange, antiquated notion
of a college of electors. How does that work exactly?
4
You need to double-down on your Dr. K reading and behavioral science in general if you wish to understand recent events like the election(s) and our polarized culture. For example, people entrench even more on their beliefs when faced with facts which disprove their own reality, especially if shared by their "herd". I'll let you tell Steve Balmer his latest data website is largely a waste of time and money since people don't care about FACTS, in light of their own beliefs and stories.
1
DL isn't being clear: A 10% risk increase is small if the initial estimate was 1% -- it becomes 1.1% (10% goes to 11%). Neither increase very meaningful. If he meant 10 % points, however, that is a much more substantial increase.
He also doesn't clarify that stats are used to assess whether a given sample experimental outcome testing a (drug, diet, training program) was due to chance and whether the results could be applied to the population the sample came from.
Say I have a sample of 100 people. I give 50 a flu shot -- the other 50 get a placebo. Let's say 15 given the shot get the flu vs 25 in placebo group (2/3rds more w placebo get sick). Sounds encouraging. But unfortunately, there's greater than a 10% likelihood the results were due to chance. So I keep going. I get a bigger sample (1000 people). Get the same type result (150 get sick vs 250). Now that result is highly significant. So, I'm more confident. I do additional research, look at medical histories, diet, other factors and find with matched samples more than twice as many who don't get a flu shot get sick than those who do.
YEA!!! However, I still don't know when I give an individual a flu shot (or don't) whether that specific individual will get sick. Population statistics do not allow me to predict individual outcomes. I can estimate the likelihood they'll get sick, but in reality all I can say is for the entire population a flu shot significantly reduces risk of flu.
5
A ton of money rides on stats and probabilities in a political race.
But I would think only 2 questions need to be polled.
1) Which candidate do you trust the most?
2) Are you actually going to vote in the election?
3
Would not work for people who would answer as I would.
Answer 1) I trust neither! Answer 2) Yes I will actually vote in the election!
Probabilities are only half the story. What matters is expected risk:that is. the probability of an event times its cost. Not always easy to quantify, but it tends to avoid the "small equals zero" mistake.
3
Using data and probabilities complemented with stories or specific examples is surely the role of all good political/economic reporters. One cannot, or at least should not, live without the other in a newspaper such as the Times.
But one thing I've learned working with environmental statisticians -- a lesson particularly relevant to our times -- is this: How much risk can you live with? Answering that question can literally mean the difference between life and death in some situations.
4
Perhaps it would be wiser not to arbitrarily ascribe pseudo-precise probabilities to events that we cannot actually predict. No one even remotely understands the trillions of variables involved in the human thoughts, actions, and interactions that may result from an action against Syria. Therefore, no one can actually calculate a true probability for any such scenario.
Since humans are inherently complicated and unpredictable, we could say with confidence that the probability of war in the mentioned scenario would be greater than absolute zero. We can also assume that the probability of war would be less than 100%. Any number in between, however, would simply be a subjective guess on the part of the analyst. Pretending that this guess is an actual, "scientific" 10% probability is absurd.
In the case of polling, a highly unexpected result is almost certainly the result of incorrect assumptions on the part of the modelers, rather than simply a low probability roll of the dice. Pollsters must assume that they are asking questions of a representative sample of the population, that they properly segment the population demographically or psychographically, that the questions will elicit answers that are useful to understand future behavior, and that people will answer honestly. They then need to put their data into a model and project behavior across the total population, making assumptions about how to weight each demographic. Easy to mess up. But not probability.
6
"Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
The problem is not with non-zero probabilities, it is with situations where you have multiple choices and resources can be focused only on one or a few, not all.
Take for instance the current Democrats growing strategy, as per this newspaper, of pursuing challenges in multiple upcoming races.
Sure, the probability of winning some of those is certainly nonzero, but, if you only need 2 additional seats in the Senate, is it better to spread your risk across many races, providing only limited funds to each, or to focus on 2 or 3 races aiming to maximize your success in those?
2
Probability is based on known facts. Despite her popular 3 million vote victory, Clinton's loss of the electoral college can be linked to as yet unknown levels of Russian hacking in 39 states - particularly Wisconsin, Pennsylvania and Michigan. Not only did Trump collude with Putin who had bought him for a song, but de facto, so did the Republican Party. An interesting probability to calculate now, is what percentage of the 40 million apathetic (pathetic is a better word) voters who stayed home 2016 want to see this country descend further into oblivion as a failed democracy.
6
Jefflz -- you have no facts to support your loony assertions.
2
Well said JeffIz, but 40 million stayed home? I wish!
The actual figure is 100 million. Out of 230 million eligible to vote.
Hillary got 3 million more? Big deal. She got 66 million, 29%.
Another way of saying that 230 million people watched a petulant toddler playing with the nuclear codes, and fewer than 1 in 3 lifted a finger to stop him.
We don't like to think about the unthinkable. Most people will still insist that Russian interference alone can not explain Trump's victory. Sure there were a few factors involved in Clinton's loss, any one of which could have caused the upset. But surely one of them was Russian interference (abetted by the Trump campaign). Yet it remains unthinkable to most of us that the Russians effectively determined the outcome of the American presidential election. But given the razor-thin edge for Trump, it's actually quite likely that indeed was what happened.
3
40 years is long enough to continue these intra-conflicts with each side of the dichotomy attempting to do the other in. May we come in from the desert and see the errors of our ways that are leading us right into the abyss. Little DiJiT is an all consuming symptom that if nothing else should focus our attention on a list of screaming priorities.
In this present crisis, story is not the solution to our problem, story IS the problem.
2
I had a statistics teacher made the arcane subject more understandable.
He used to say, "It is not difficult to lie using statistics. The trick is to not lie to yourself." -Professor Thorpe
You can help people understand probability and statistics, but there is not much you can do for those who are dead set on lying to themselves.
8
and we wonder why it has seemed so easy to convince so many people not to trust scientists, when they think in terms of relative likelihoods, rather than "proof."
Many of the letters already written stress the need for both probabilities and consequences when considering a course of action. I look forward to a next column addressing that.
1
There is wisdom in foresight, none in hindsight, except that you can rebuild stronger on its behalf.
As a biologist, I’ve worked with (statistical) probabilities most of my life and have no need for a story to interpret them. But in our daily lives, I understand the need for more explanation. Years ago, I queried the National Weather Service asking how to interpret the probability of rain in their forecast. They said that it was the probability of getting wet if I stood in one spot all day. That’s not how I lived my life; I drove to work, went out for lunch, went to the gym and drove home. Calculating my probability of getting rained on was much more complex, so I took the weather forecast as general guidance, which is what it is.
Stories about probabilities don’t always help us live our lives. Our lifetime probability of being killed in a vehicle accident is 1 in 113; of being killed by police is 1 in 8,359; of being killed by a foreign-born terrorist is 1 in 45,808 (http://www.businessinsider.com/death-risk-statistics-terrorism-disease-a.... Even though we read that, many Americans live in fear of a terrorist attack. Stories in the media only stoke those fears. We blithely accept (or ignore) the lifetime probability of dying in a car accident, but we buy guns, avoid foreign travel and live in fear of being killed by a foreign terrorist. Mr. Leonhardt is correct, we need better ways to present probabilities and more education in probability theory.
10
Mr. Leonhardt's final paragraph insults the integrity and competence of President Obama, tacitly accusing him of using his government position for political purposes. The Obama Administration did notify local election officials of potential cyberthreats and offered to help mitigate those threats. They could not overtly and publicly counter Russian interference during the campaign, because such action would have disrupted the election. They were, however, working behind the scenes. It's time to retire the tired old Hillary Clinton mantra that everyone and everything except the candidate herself was responsible for her loss.
And that all occurred in 2016, well before the start of the year that is now coming to a close.
2
Well, we know you & the NYT were wrong last year about the election. And it was not because your analysis was faulty, it was because you believed that there was no way that Trump would take all of the battleground states. The day before the election the Times analysis indicated that Clinton had an 85% chance of winning. It showed that Trump would have to win the battleground states as well as Michigan, Wisconsin & Pennsylvania. Virtually no one thought that was possible. Even Trump was skeptical of his chances of winning. Yet it happened. Why?
Because there were enough Americans voting in just the right states who believed that the country under Obama was heading in the wrong direction and they ignored Trump's character deficiencies and put an outsider disrupter in the White House who had an entirely different perspective on how to govern the country. And he has amply fulfilled their expectations.
The trade off has always been having to put up with Trump the person in order to get Trump the reformer and disrupter, the scourge of Washington, D.C. Now that we have him, how well will we endure him & his aberrant policies. Only the 2018 election will answer that question.
3
"Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
Bingo. And if Hillary had won there would be no investigation of Russia's meddling in the election.
1
A: “Estimated probabilities” is redundant.
B: There’s another, simpler, truism at work here:
In a universe billions of years old, that will exist for billions more, Everything that CAN happen eventually WILL happen.
As a basketball fan I've seen a lot of slam dunks missed off the back rim. Doesn't mean you shouldn't do it if you get the chance. It's the highest possibility of scoring
que sera sera. It doesn't make one iota of difference in the FINAL outcome of anything, if one was right or wrong. (unless of course, you are making a wager) Many people believed that trump would NOT become president, the RISK was low, and yet, in the final tally, he won not because of the popular vote which we keep track of, but the vagaries of the electoral college system.
It is best to keep in mind that no man may know what another man is thinking, and only real outcome in the one that happens. Then you must deal with it based on YOUR notion--not mine.
Between the stock market and sports we seem to be obsessed with numbers in all the wrong places. We not only got donald, but the damage he is doing is nearly unfathomable and there is no amount of second guessing as to what the end will look like. What are his chances of being impeached? What are the chances that KONGress will do its duty and toss him out? We can spend from now until next Christmas trying to get the numbers but that just fills the otherwise useless pages of the newspapers around the nation. Actions speak louder that words or numbers and the coutcome is the only reality.
But David, what does it mean when 97% of scientists believe in human-made climate change, but over 50% of our elected politicians in Washington round that number down to zero?
That even the clearest numbers cannot overcome superstition. Yes, humans need a story, and the one that they recount today has sustained many generations in their self-regard as they mistreat those outside their sanctified circle.
Scientific investigation often returns uncomfortable results. Therefore, the word scientific has no place in modern government. How can we MAGA when science tells us we aren't?
And just as the Romans did over 2000 years ago, we kill the messenger when the message is that we need to take stock and change if our descendants are to survive.
Tell us lies. Tell us sweet little lies.
7
If I only do things based on the probability of success, I would have stayed at where I was and continued my unhappy career path. Of course probability is an important consideration. But more importantly, I always vote and I don't take chances. Elections have consequences and I knew better. Back to my career, my hunch is often correct but I never run serious analysis. I just "feel" it. The key is to put myself in other people's shoes and think what they would do. Also honesty is the best policy and long term planning is better than seeking immediate returns. Character, integrity and perseverance are all important too.
The problem I see is people are doing too much calculations. How to maximize returns by putting in minimal amount of effort is what people usually think. It is very sad that we come to this point. How about just honestly work hard and let God/fate/whatever decide the outcome. If it is right, just do it!
"Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
They might have taken Russian interference more seriously if they hadn't been too busy polishing up their resumes in preparation for their upcoming careers on K Street or Wall Street.
The election of Trump, and a Republican majority has the distinct feel of impending destruction.
Their shared persistent efforts to make money in this presidency, profiting directly or indirectly, is a scandal that cannot be let go.
Republicans initially viewed the Trump campaign as a mildly amusing temporary sideshow.
Now they are in deep, and quite corrupt--with the House of Representatives skating off the Trump-Russia ice rink and now maligning Muller and others.
And how Republicans praised Trump on that tax bill as if he is North Korea's Dear Leader.
Having not long ago met to discuss how they didn't want Trump near the nuclear codes.
The GOP is now a dangerous lockstep herd.
1
Whether we understand probability or not, we live in a probabilistic world. Policy makers, and the voters who hire them, need to internalize that fact. If we require education to understand probability theory, then we must obtain it. By all means, amplify the lesson with a story, but we must understand at a deep level the nature of our world. As voters, we must reject simple answers and the charlatans that propound them. Those simple, uninformed answers offer only danger shrouded in comfort. The probability of that danger being realized is about .99.
As "probability" is currently understood mathematically as a particular type of integral, i.e., the area under a probability distribution curve between two values, the probability of any single event cannot be assigned a value other than zero.
Colloquial predictive actionable psychologists' "probability" talk, without adducing specific complete physical causative facts, is actually nonsense, as was a "10% probability" of "war," or an "85% probability" of winning a specific election, or the success or failure of a specific medical procedure in a specific single case.
Arthur Taub MD PhD
Clinical Professor (ret.)
Yale University School of Medicine
1
I think the key here is that in most cases there is no "correct" or unique probability for a given outcome. (The only exceptions I can think of are quantum mechanics and certain games of chance.)
The probability in part depends on your knowledge of the situation, or the sample space, and therefore can vary. For example, the life expectancy of a person (which is related to probability) can depend on, e.g., whether the gender is male, female, or unknown. You'll get three different numbers, all correct w.r.t. their sample space.
Or consider a disease that kills 10% of all who have it. If we have 1000 people about 100 will die. Suppose we later find that 10 people contain a protective agent in their blood that reduces the probability of death to 1%. If we don't know who has the agent, the probability of a given person dying of the disease is 10%. But if we know the person has the agent, the probability is reduced.
So a given probability, aside from the exceptions noted above, can be "correct" _only_ w.r.t. the specified sample space.
1
What's needed here is the discipline of risk analysis: risk is probability times consequence. A 10% increase looks a lot less desirable if the consequence is catastrophic.
9
I agree. People will always tell you that your chances of bring eaten by a shark are minuscule, but in the moment, if it happens, it is so horrific that the numbers pale in comparison.
I rarely enter the salt water.
2
It's nice to see that some understanding of probability is making its way into general discussion. After all, quantum mechanics is more than 100 years old at this point. Nate Silver made it very clear. He had HRC ahead by a few points, but had the odds of Trump winning at about 30%. 30% is a very substantial probability. It is almost one in three. HRC needed to be at about 50%, or slightly greater, not 48% to lower that 30% probability substantially. She was not for many, many reasons, most of which were not her fault at all, IMO.
2
In saying that "explanation is doomed to fail," you appear to assume that the only thing that can count as an explanation is a statement of probability. That's just not the case. In searching for an explanation of why something happened--for example, Trump's election--we look for factors that brought it about, not reflections on how likely it was to be the result. True, if we want to produce or prevent another occurrence of an event that has occurred, we'll look at factors that seem to make such events more or less likely. But once something happens and we want a satisfying explanation of why it did, our immediate concern is not how likely it was or was not, but why in this case it occurred. (Here endeth this alleged explanation!)
3
I teach business research courses. The one lesson I want students to remember is that numbers are usually necessary but virtually never sufficient to change minds. If you use statistics, probabilities, correlations, etc. to influence someone, the best you can hope for is that you will catch their attention with a number. The ONLY thing that ever changes minds is stories and personal experience. Trump's numbers are always wrong, but his stories and promises speak to the heart of half of the American voters. Logic, intelligence, and rationale never win the day. It's always about the incentive behind a story. Game theory/behavioral economics explains this quite well.
18
The ONLY thing that ever changes minds is stories and personal experience."
If that were even vaguely true we would NEVER AGAIN have a school shooting or mass murder. People would give up their guns never to plug a nickle again. Of course, we know that stories are good for raising money for those injured or in need of a casket, but a potential shooter --say a 51%-er, is not going to be swayed based on the Sandy Hook shooting. We may get robots to memorize the encyclopedia but they never be as complex as the illogic of humans--that is what AI can't do--human illogic.
Cheddar, I agree...but...what IF, the numbers were truly made a more important part of the stories? IMO, at this moment in time, we as a culture are enraptured (distracted) by far too many stories, with far too many ways to interpret...leaving us with nothing but opinions, based on feelings.
What IF, we started to cut off the feelings based interpretations - with facts, numbers first? Bring the numbers, and facts to the forefront...then fill in with the stories...
????
1
Given that his stories are at best hallucinatory and at worst racist, and his promises are a pack of lies, we'd better hope that that is not what speaks to the hearts of half of America.
2
I knew Hillary Clinton was going to lose. I knew that by making the election about personalities—Clinton (slandered by the GOP-held Media for 30 years) vs. Trump (the great manipulator and TV showman) most ill-educated Americans would think it was some sort of personality contest and vote accordingly. And they did. My suggestion to the Democrats is to make elections about Platforms, not Personality.
86
Re : in reply to Ravenna
Actually, when I saw the statistics for the 2016 election, I was horrified to see that it was not Trump who had magically convinced more people to vote for him. In fact, it had been millions of Democrats who had voted for Obama in 2008 and 2012, who either stayed home, or voted for third parties,(Communists, Greens for Sanders), who sank the Clinton Candidacy.
Somehow, the insults and the lies of Russians, Rpublicans and other BS had managed to convince all these Democrats-over13 or more million-that Clinton was too conservative-or that she had stolen Obama's third term,(I know there is no third term-but many voters don't)
It was these angry and suspicious Democrats-ensured by the Newspaper of Record of her victory-who allowed an extremely surprised Donald Trump to win.
It still took Democrats a month-just as in 2000 and 2004, to realize that the fools among them , had given the GOP the election. again they tried the legal approach , but our electoral system is guaranteed to benumb the sharpest minds.
And Because Democrats are so hypnotized by a search for the perfect candidate-Martin Luther King jr. mixed with JFK, that they will settle for no less. Because we'd rather fight then agree, we are ruled by dullards who make Scrooge seem saintly, most of the time.
2
the only platform democrats seem to know these past decades is one on which they serially hang themselves out to dry. BIgly SAD.
Wait - I thought making elections about platforms bores "the people" and "personalities" seem to have quite a bit of success - any probabilities here?
1
Great column. I would like to make two points.
Grasping the statistical likelihood for even for the simplest of problems can be counterintuitive. With the famous Monte Hall Problem, where there is a choice of keeping your original random choice or switching (after seeing what's behind one hidden door of three) some of the greatest mathematicians have come up with the wrong best choice by not correctly applying Bayes Theorem of conditional probability, or by brute force listing all 6 possible outcomes and simply counting wins and losses.
Decision making creates a complex matrix of possibilities. Go to war and you'll win say 90% of the time. But the chance of no casualties may be 5%. The chance of it causing an economic recession may be 50%. The chance of losing the next congressional election may be 80%. How can one process all these probabilities? You could weight them according to significance and come up with one set of odds of a good overall outcome. But, political leaders tend to make these judgment calls based more on instinct. If they have good instincts, these may well correlate well with statistical predictions. If they shoot from the hip like our current selected president does, you might as well flip a coin, because like a chess player who thinks zero moves ahead the winning move is not to play.
7
Almost all the probabilities one used in everyday life are meaningless, because they are not quantitatively demonstrated, but only someone's attempt to quantify his story (gut feelings). In Kahneman's story, how did the analyst make his estimate that the probability of war would increase by 10%? That would only make sense if he had run the experiment, with and without the proposed action, many times and compared the outcomes. You can do that when you load a die or coin, but not with war.
For example, someone says he is 90% confident of some outcome or explanation. That only makes sense if he has made a large number (perhaps 50--100) of comparable explanations, and found that he was right nearly 90% of the time (for example, between 87% and 93%). That never happens (how could you know that they are comparable?). So translate such false quantification back into words: he is fairly sure based on experience and reasoning, but admits an unlikely chance that he might be wrong.
False quantification is worse than no quantification.
Jonathan Katz
Professor of Physics
Washington University
St. Louis, Mo.
22
Dr. Katz;
Life is not a scientific experiment and can never be. However, most of us need an understanding of what is likely to transpire given what we 'know,' just so that we can be prepared.
As soon as Mr. Trump declared his candidacy, my wife said, "He is going to win, you know."
That is all that I needed to know.
Regards,
gerald
9
I'd also point out that the numbers only tell you what the numbers tell you, and that it's necessary for people to add in the guardrails and meanings.
Good point. The "increases chance of war by 10%" was simply an attempt at quantitative expression of a story the researcher had told himself. The suggestion that pundits when saying something is a long shot should also provide a scenario for how it might happen is a good one. For example, "Trump has only a 20% chance of winning. But if we have underestimated how support among former Obama voters in the midwest, then he has a good chance of winning." If you show how your prediction might be wrong, its hard for others to say you were wrong especially if you correctly identified how you might be wrong.
I like to embrace serendipity rather than probability. In my introspective (albeit rare) moments I like to reflect on events that, in hindsight, have resulted in considerable consequence to the course of my life. I tend to view the results from serendipity (a que sera, sera attitude) versus a carefully planned series of events from the perspective of ultimate outcome.
In virtually almost every reviewed situation, I have found the outcome from serendipity to be far more positive than a carefully planned event. True, it may be as a result of being a really bad planner but I like to think there is a more karmic explanation or perhaps simply good luck or perhaps a guardian angel interfering with the odds. From choice of area of study at Uni (the Bus Admin registration line was shorter than the Engineering line; to my spouse we met at a bar and never really parted; the house we bought, the price was right, who knew the area would be trendy 30 years later; to children, again que sera, sera and now we have two successful beautiful daughters.
With regard to Mr. Leonhardt prognostications, I think that a 90% probability that Mrs. Clinton would win must be considered a slam dunk, and the failure of that prediction should result in a very serious examination of the methodology used to arrive at it. Although I guess that it has a 95% chance of being right. Personally, I think que sera, sera.
6
If you never think about the counter-factual then life is good - but you have to think about the counter factual to be rational.
1
Serendipity means no counter factual at all. Being serendipity it is an unplanned event. To react to the counter-factual would remove it from the realm of serendipity. That's the point.
How many people in Pennsylvania, Michigan and Wisconsin either didn't bother to vote in the 2016 election, or voted for a third party candidate, as a result of the polls that said Hillary had more than an 80% chance of winning? In this case, it is likely that polls themselves affected the election. If you believe that the desired result is a virtual certainty, it frees you to cast a protest vote or not bother to vote at all. I hope Democrats have learned something from this disaster.
26
How the Democrats Gave Away the 2016 Whitehouse:
If the Democrats had avoided one or more of the following three incompetencies they would be running the government.
Allow incriminating emails on the DNC web site and have incompetent cybersecurity.
Have a candidate who did state department business on a private email server with no obviously good reason.
Have a candidate who affronted the voters that were needed, e.g., the “deplorables.”
1
Hillary’s campaigns fundamental error was not simply based on a misreading of statistics and probability. Her fundamental error was based on a misreading of basic accounting, economics and biology. That is what translated into her loss.
She never got the basic economic fact that opening doors to millions of illegal immigrants DOES cost 100’s of billions of dollars in associated social services every year. When she presented a single mom illegal immigrant with 4 kids as being a hero, I groaned. Each of those kids costing 10,000$ a year to educate. And that is just the tip of the ice berg.
When she ignored the impact of population explosion over 300 million people in the USA and fast heading to 400 million while bemoaning climate change; she again showed a total lack of scientific understanding. Too many people cause climate change, climate change does not cause too many people.
I know someone who bought a house outside Los Angeles bordering the wilderness that is now in flames. When they first moved in some coyotes who had lived there could be heard howling each night at the theft of their range.
Across America we push every living thing to the brink of extinction with our growing numbers. We pack surviving animals into hellish conditions to feed our numbers.
Not being aware of all those things cost Hillary the election, not simply statistics.
16
climate change does not cause too many people."
IT could though if for some reason we has no sun for a month. Remember the blackouts in NYC in the 70's--there were a lot of children born the year following.
Ben Ross: Given the fact that we are not reproducing among our Anglo Saxon population, we now rely on immigrants to raise families, run businesses, buy products and pay taxes. If you believe immigrants do not pay taxes, you are believing Fox News garbage. And, those "illegals" you all complain about are working for big developers and contractors who want to pay low wages with no benefits. They use the illegal work force and send them home after the work is done. Those who manage to stay continue to work for low wages and no benefits. Hillary Clinton didn't open the door to poor immigrants to flood the East Coast; the business community on the East Coast opened that door to exploit cheap labor; the cheap labor swarmed in, because they are dirt poor and have no safety nets. We have exploited the countries they are coming from; now we want them to stay there and starve.
Sigh. Here's the deal: first, the oldest American story there is, is immigration.
Second, if you're gonna make up numbers, make some up about the kids from Africa who came to this country a few years back, knowing no English. We're all going to be helpng send three of the to the Ivy League colleges and universities they worked their ways into.
You tell me: what's the return on that investment likely to be?
Oh, almost forgot. Can you point me to the part of the Constitution where it says, "be miserly and short-sighted, and always put the dollars first?"
1
The most frustrating conclusion that Daniel Kahenman offers is that after decades of studying these types of errors, he cannot catch them in himself. He says so in "Thinking Fast and Slow" and I have even heard him say so at a talk. That is the human condition. For better or worse, we get better at catching these errors in others but not ourselves. It would be nice if that engendered more humility but that my be part of the human condition too.
7
Perhaps what is missing is the law of averages and good old common sense from some of these fancy probability ideas. I see the media pundits underestimating the average American's ideas of what is good for the country and what is working. I see them heading in wrong directions about what is important to people. I see them relying on polls from heaven knows where instead of talking to people. It is always interesting to see how often they are way off course in their conclusions.
1
"I see them relying on polls from heaven knows where instead of talking to people."
It appears that you don't understand the process of polling. They get their data from talking to people.
The issue is with sampling. You won't agree with a poll if the people you talk to are different from the ones the poll got information from. That's where polling science comes in. They are supposed to get responses from a representative cross-section of the intended population, so that the results approximate the entire population. The sampling doesn't always work.
Challenge: define "probability" without just using a synonym, like "chance". Not many people can do it though there is a mathematical definition. Probability means that as the number of occurrences increases the ratio gets closer to a particular ratio, which we call the probability. That is all it means. It is only useful in the case of multiple occurrences, for example, for the bookmaker to determine the odds on a horse winning. But it is useless in telling us whether a particular horse will win. And it is useless, though often applied, for telling us our probability of survival following a medical diagnosis.
3
well - no - there are three generally accepted models of probability and you seem to be describing one of them.
if any of you want to know more there is a most excellent MOOC provided by UC from EdX going on now about Bayes
1
Probability does not tell you directly about your n=1 survival after a medical diagnosis. But you can still use it to train yourself to stop worrying about survival. Get a number from the doctor, check the arithmetic (yes, mine was 10 points too low due to addition error), adjust it a little for all the things you know about yourself that the oncologist does not know, and then stick to that number. Repeat it every time you ask yourself irrationally how long will I live -- answer yourself that I have a 65% chance of living 10 years (or whatever probabilty you have chosen). At first you have to answer your irrational question many times a day. Then it is just once on waking. Then, on waking, you think the answer before the question occurs. After a couple of years you stop asking yourself this ridiculous question. I think the key is to have a believable answer at the start, as if the question were rational. Then gradually you stop asking the question because you are fading back to normality and you do not need an answer anymore. So, ime, the probability is useful only in weaning yourself from fear of the future.
"I think part of the answer lies with Kahneman’s insight: Human beings need a story.
It’s not enough to say an event has a 10 percent probability. People need a story that forces them to visualize the unlikely event — so they don’t round 10 to zero."
Perhaps a problem at the NYT is that it mostly presents stories that it's paying liberal base wants to read--stories that agree with its world view. Thus, these readers are not "forced" to visualize the unlikely event.
Trump's triumph was a horrific shock to so many NYT readers because so little reporting had addressed the discontent and anger and frustration during the eight years of the Obama presidency in all those states between the coasts. Instead there were so many stories about how well the country was doing under Obama and what a great, transformative president he was. Negative or critical stories appeared briefly, or were not reported at all.
To prevent future trauma to its loyal, paying liberal readers perhaps the NYT might consider providing more even-handed coverage of the world, should an event that its reporters/editors/columnists feel is highly improbable or impossible occurs (e.g. Mueller discovers that Trump did not collude with the Russians before the election).
When readers are provided with only the stories they want to hear, assessing probabilities becomes even harder. Such pandering certainly helps a news organization's bottom line, but it does no service to its readers.
13
"Such pandering certainly helps a news organization's bottom line, but it does no service to its readers."
Echo chambers are worthless.
Excellent! How many acknowledged Republicans or Baptists are in the news room?
I am a woman who was born and raised in one of those states between the coasts. None of my family, going back three generations from me, has ever lived anywhere but the midwest. Wanted to point that out before I correct you on your multiple paragraphs of misinformation.
Trump's electoral win was a horrific shock to the majority of Americans because of the factual and op-ed reporting (nationwide) which affirmed that Trump was unqualified and unfit for the role based upon his business record.
I recall several news articles which were then backed up by stories from small business owners who were forced out of business based upon Trump's inability or refusal to pay for their services. I recall several pieces where his discriminatory business practices (information pulled from legal records), was backed up by stories from those who were refused housing based upon their race.
Perhaps you are not a long-time/consistent reader/subscriber of NYT. Do a search in the NYT archives. There are plenty of critical articles and op-ed pieces about Obama's Administration and Policies that include "stories" from Joe public. Incidentally, did you sleep through the entire process which brought us to Obamacare and the aftermath? Do you not recall reading article after article regarding the public's reaction?
How about when the banks and car manufacturers were bailed out?
Or when he decided to start using drones?
Until Americans know just how much the Russian interference determined Trump's win in the election, this entire discussion is nothing but speculation. Until someone proves to me that American voters really did put Trump in office on their own--without Russian interference in the election results--I'm really not interesting hearing this guesswork.
5
It appears as though you, like many, have come to the conclusion that the only way that Trump could have possibly won was with the assistance of the Russians. Consequently, you are demanding proof of a negative to overcome your denial.
Vladimir Putin is gratified. This is the chaos that he sought.
A similar scenario would have followed a win by Clinton, absent a Grand Government Inquisition of course. Belief in Putin's hand would have been written off as a crazy conspiracy theory since Clinton was the "rightful heir" to the Obama Legacy.
2
I voted for Trump's policies not for the man.The Russians did not influence me.HRC's shady deals and lack of good policies did influence me however.
1
Coming to the conclusion that Trump's win was due to Russian assistance is a kinder explanation than saying that those who voted for Trump were incredibly irresponsible at best or incredibly stupid at worst. Perhaps both are equally valid.
But What About The Algorithms?
I would like to write a long essay criticizing this article, but it would be waaaay too technical and, therefore, uninteresting to the typical NYT reader.
Consider the problem of making a political decision. The analyst starts by identifying important constructs that might have an impact on the decision and those constructs that will be affected by acting on that decision. These choices are invariably incomplete, so that part of the process is subjective ... we are already once removed from reality. Then we must operationalize the constructs and measure the variables ... now we’re thrice removed from reality. Next, we collect data (with the myriad difficulties of doing that correctly and well), choose our analytical tools, and then, up to some degree of probabilistic “certainty” and making seat-of-the-pants adjustments for analytical assumptions which must be met (but rarely are), we draw our statistical conclusions.
Now we have a statistical decision that is at least six times removed from reality. If we think all of this makes sense, we should be prepared to make the gigantic leap from our model’s conclusions back into a real world in which the consequences of the decision will affect jobs, incomes, families, communities ... even lives.
I encourage you to ask Robert McNamara how that works ... for a CEO of Ford Motor Company ... or for the President of the World Bank ... or for a Secretary of Defense managing a war, say, in Viet Nam.
7
While the title suggests some "mea culpas", what we actually got was some reasons for being wrong, not what the wrongs were.
A probability lesson is not what I expected or wanted.
That said, I'm not counting on any of the other NYT pundits to fess up either.
5
“No one ever made a decision because of a number. They need a story.”
And today's story is that 95% of Americans talk to like minded people 92% of the time (yes I made those numbers up, but you get the idea). And when the story they get from their friends and favorite media sources don't match the result (ex: Trump wins; Hillary wins the popular vote by over 3 million), they cry "rigged!" and sometimes "fake news!" Particularly when the probabilities/polls predicted otherwise.
You never change a religious person's mind with argument. They have their story, and they're sticking with it. Today's politics are akin to religious beliefs. Don't confuse me with the facts, heathen!
www.newyorkgritty.net
13
There’s something else going on here besides probability. The establishment media was shocked when Trump won not because of probability but because they didn’t know anyone who voted for him. It’s another bias that prevented them from reporting the story.
15
I think the bigger problem was overestimating Clinton's negatives in an anti establishment year, after she crushed the hopes of millions of Bernie supporters, mostly, young who really didn't want the ultimate establishment candidate.
8
That is true. The possibility of actually going out and interviewing people liveing between Scranton and Los Angeles and finding out their concerns was evidently a prospect too odious to contemplate, even for interns. Mrs. Clinton's offhand treatment of Michigan was inexcusable. So now we have an enormous amount of anger and division, with neither side willing to understand the other. I am 71, and am truly afraid for the future.
Actually I do know people who voted for him. Many are naive elderly women who always were dependent on the men in their lives and others were just plain bigots who hadn't gotten over the election of Obama. Some were older men who want their women subservient.
Probabilities multiplied by costs/values of outcomes...Expected values/costs.
That’s the next step in decision making via probabilities.
War? Very expensive outcome, and a high expected cost (even there is only a 10% chance of it happening).
3
Most studies on how human beings (even experts) evaluate risk (and probability) address not the rounding mentioned here but the relation between desired outcomes and risk. People have difficulty evaluating outcomes with low probabilities that they consider disastrous or highly undesirable. Low probability disasters always seem far more likely than the calculations indicate, while high probability events to which we are indifferent frequently seem less likely. Some probability theorists push the math. I think people's intuitions are much more useful. The top official was expressing his views, largely uninfluenced by so "low" a figure as 10%. The story matters much less than the moral and cognitive stance of the person responding to the risk.
2
It’s the severity of the pre-existing state or the outcome that colors the import of the probability estimate. A patient with an incurable fatal cancer will embrace a therapy that gives a 1% probability of survival . I might also think twice about a plane ride that has a 1% chance of crashing.
3
I believe in chaos theory. Chaotically Trump won, and chaos rules.
8
Well, what exactly *were* you wrong about this year, Mr, Leonhardt? I was expecting some critical self-reflection, but you merely delivered the old wisdom that probabilities are hard to grasp...
15
The fact that nothing is certain is a scientific fact probably best embodied by Heisenberg's uncertainty principle.
However, authoritarian regimes and the average person in the street want complete certainty. That's how Bolshevism in Russia, fascism and nazism in Europe, and currently Trumpism in America have gained their adherents: offering the masses the complete certainty they craved for during times of hardship.
Complete certainty has also been the opiate offered to the masses by ultraconservative religions from Catholicism to Wahhabism.
Scientists have been attacked and/or oppressed by authoritarian regimes and ultraconservative religious movements, because they refused to bend to dogma and asserted uncertainty.
The path to the truth can be a long and painful journey, but one can take solace in the fact that in the end science and/or justice prevail.
12
That is not what Heisenberg was postulating.
1
‘We need a story.’ Maybe. I think we just don’t understand what probability means. It doesn’t tell us what to do or how to feel. (How do I increase the probability X will win? My candidate or team has a 55% probability of winning. What should I do now?)
1
for an interesting read about the way statistics can be used to mislead, read "Proofiness"
3
An old classic is "How To Lie With Statistics".
Fukushima is the best example of flawed reliance on risk probabilities. A very small likelihood of an incredibly disastrous result. But magical thinking and denial play their roles as well. Right now the most dangerous risk facing the world is that of nuclear war with Korea. But it is literally too horrible to imagine. So Congress does not take the nuclear weapon button away from an unhinged man child and turns a deaf ear to his insults and taunts, triggering a fearful exchange of threats with North Korea. And the rest of us are frozen in hopelessness. The problem is not just probabilities, it's much more.
8
"Alas, unlike a dice roll, the election is not an event we get to try again."
A parliamentary system can trigger a "vote of confidence" when things go awry. A chance to remove an obvious stain.
Alas.....If only the Founding Fathers had..........
6
The two-party situation resulting from our system of government is largely responsible for the political polarization plaguing our country. In this winner-take-all system, one party wins by the barest of margins, in an election tinged with illegitimacy, and they rule with an iron fist, as if they won by a landslide. I think having three or more political parties of sufficient size and influence would result in a much more representative government.
It seems that a parliamentary system might be more likely to create this result, but there may be other paths toward it for us.
If we got rid of the Electoral College that might help matters by removing one huge opportunity for mischief.
Did I miss the part where he talked about what he actually got wrong?
15
Probably.
Don't feel badly, that makes at least two of us.
1
"Alas, unlike a dice roll, the election is not an event we get to try again."
Yes. Or aveering a nuclear war with North Korea. Or redoing climate policy to avert disastrous effects of human caused climate change. Etc.
7
Do you have any suggestions of what individuals can do to voluntarily reduce our CO2 emissions by at least 50%, let alone by the 90-95% or so required to stabilize atmospheric CO2 levels?
Nothing stops people from doing individually what government does not mandate them to do by law. I'm all for constructive suggestions, if you have any.
My concern is that the NY TImes seems to have assumed Hillary would win and, as a result, not bothered to report the overwhelming evidence that Donald Trump was unfit to be president. As a result, you focused on her emails and alleged health problems and went so far as to totally deny that there was any issue with Trump and Russia. How can you write this commentary and not acknowledge what the Times did?
11
Maureen Dowd gets and extra swipe for her totally unnecessary vendetta against Hillary Clinton....snarling and clawing at a woman who was only trying to run for President. Wait....maybe that was her great error....to run for President while female.
1
Thank you!
1
In defense of the NYTimes, the vast majority of media outlets were complicit in this.
1
Probabilities always need a context. If one scenario increases the probability of war by ten percent, we should know what the existing probability is at baseline. Probabilities are often inaccurate because of the impossibility of considering all variables. Consider not only Trump's improbable victory, but Karl Rove and company's shock at Obama's win. In fact, polling, which often figures into "probable" odds, has become less reliable over time.
Probabilities are much easier to figure when dealing with decks of cards than when dealing with human beings, and probabilities go out the window when dealing with capricious behavior. One of Donald Trump's fundamental tactics is the constant threat of acting in improbably dangerous or stupid fashion. Such tactics enable him to extort compliance through what amounts to psychic blackmail. It's a major reason why he should be removed from office; he can be counted on destructive behavior often enough to represent a clear and present danger to the nation.
9
David, It looks like you have not really learned as much as you think you have. If you had really learned the lesson of 2017 it would be not to make statements you cannot support with evidence. Polling data is evidence of answers people gave the poll-takers. In other words, if a bunch of people were doing an Improv session, one should not try to extrapolate how those folks would react in a real situation. They might do something very different, and they did during the real election.
Your comment about Obama administration officials "might have treated Russian interference more seriously ..." assumes they had a whole lot of choices available to them which would have affected things only positively and nothing at all negatively. But in reality, anything the Obama administration did (or even did not do) regarding the election was under constant attack by the right-wing media, especially the sacred cows on Fox News Network that none of you "mainstream" media folks had the guts and decency to challenge head on. Put bluntly the Obama folks had no viable choices. It was Hillary's job to beat Trump by 20 points and she failed. Look at Macron for evidence.
So, in conclusion, the lesson of 2017 is do not take anything for granted - not rubbish on Facebook, not rubbish on Fox News and not rubbish on NYTimes, CNN, MSNBC, and others who gave Donald Trump over $2B of free advertising. Step away from your column for a few months, avoid the noise and haze, and start seeing more clearly.
12
More importantly, probabilities are moot with a rigged deck.
6
well no - you can develop a perfectly fine probabilistic model about a rigged deck.
1
I think the idea of predicting this stuff as "probabilities" is nonsense. Saying a candidate's "probability" of winning a specific election is 33% means that if you held the election 3 times he would win once. But in the real world the snapshot of the electorate is in place whether we see it or not and there is only one possible outcome... and that outcome is guaranteed, even though we can not know in advance.
4
Anecdotal evidence is the bane of statisticians. But anybody who saw the Carrier plant meeting on TV, where prior to the election management announced the closing of the Indiana plant and relocating it to Mexico, knew the Democratic candiate and party was in trouble. The raucous reception of the bad news by the assembled workers was a tell for the way the midwest would vote. To do statistics right you need to assign the proper statictical weights to the input data.
1
I once heard Billy Graham make a theological point by using percentage. I’m paraphrasing, but it went something like this: Let’s say you’re on a plane from New York to Paris; just before takeoff, the captain gets on the intercom and says “Ladies and gentlemen, just wanted you to know that there is a ten percent chance we won’t make it to Paris.” Would you stay on that plane?
Even since hearing that (in my teens), I realized that “a mere 10%” seems a lot more dire and more likely to occur if the outcome could kill you.
2
Over and over again, we prove not to be Homo Sapiens—thinking man. Rather we are Homo Fabulans—story-telling man. People remember stories, make decisions based on stories, and make up stories to justify their decisions and feelings. If the facts don’t fit the preferred story, a story is created to discount those facts—and probabilities make that process just so much easier. Math is hard, but it will be the end of us if we don’t manage to become that aspiration—thinking man.
5
Probabilities tend to be devastating to some of us if they are wrong, witness the barbarian ignoramus winning the White House on false pretenses and supported by credulous and resentful folks we didn't see coming. Ought we perhaps be skeptics looking at mere possibilities instead? And knowing via common sense that scientifically identified statistical samples of city folks cannot attest to the wishes and needs and prejudices of the suburbanites and rural left-behinds? Losing our objectivity by hypnotic candidates perverting reality was not in the charts, was it? As Black Swans aren't...until they do.
3
Many of these comments prove that even highly intelligent people can fail to grasp the connection between the probability and actuality of an event's occurring.
A 95% probability of rain means that, in any set of 1 million days with identical meteorogical conditions, there will be 950,000 days of rain -- and also 50,000 days of no rain.
This means, then, that a single dry day does not prove the predicted probability to have been "wrong." After all, the 95% chance of rain was inherently a prediction of 50,000 rainless days in the group of 1 million days being studied.
Rather, the assertion of the 95% probability of rain is "wrong" only if the ratio of rainy days to dry days during that million-day period is different significantly from 95:5.
So, if, over a period of 1 million days, a half-million days are rainy, and the other half-million days are dry, then the initial prediction of 95% would have to be considered "wrong." But -- and this is the key! -- the existence of a single dry day in no way invalidates the original prediction.
The assertion that Hillary Clinton had an 85% chance of winning meant we should expect her to lose 150,000 times over a period of 1 million elections with identical facts and premises.
That 85% probability of a Clinton win was not invalidated by the result of a single election's loss, just as a 95% chance of rain is not proven wrong by any one day of sunshine.
8
Since there was no other instance, never mind one million instances, of a Hillary-Trump election, assigning a probability with a certainty within 10%, never mind 1% (which is what 85% means) is idiocy on stilts.
One simple way for The Times to help people understand the numbers in news stories would be to provide the absolute dollar amount AND what percentage that represents of the whole. I really hate it when a story gives the reader only one or the other of these numbers. You cannot determine the value or importance of anything without at a minimum BOTH OF THESE FIGURES!
1
Mr. Leonhardt fails to mention that big data is only as good as the stuff collected, ye olde garbage in garbage out.
In polling before the last infamous presidential election, pollsters now think they were getting a lot of lies from people who intended to vote for Trump but wouldn't admit it. For some reason.
Probability and statistics are worthless if the assumptions are based on alternate facts, or what used to be known as lies.
9
Mr. Leonhardt writes so very nicely about a debate that frustrates many with some science background. To wit:
Does the exception prove the rule?
Or does a single exception disprove that rule and, worse, all rules?
'Reason' requires probabilistic analysis as it simultaneously accepts 'being wrong' as the essential risk.
We are NOT all knowing. Only fools and charlatans make that assertion.
And so, let us pray, as we make choices based on acceptable versus unacceptable risk, and accept our result as part of the dynamic of living.
1
Beyond probabilities is a dimension of critical concern. A 10% chance almost equals zero about concerns that matter little. It is huge if the concern is a catastrophic war. This is also a political dimension. It is worse to be wrong about something critical, especially if there is a clear line of command. Which is why so much propaganda is about diffusion of, or outright lies about, the critical concern when something goes wrong. Which is why values matter and why stories we tell (and accept) matter.
2
In politics, probability's usually speculation --so that gets frustrating. Probability's more quantifiable. It looks for certainty.
It made no sense an undeserving, unfit Donald Trump could win the presidency.
With Russia, Wikileaks, + use of data analytics aided by Russia, Facebook + Twitter, Trump attained advantage--and "won." And that is very hard to live with.
Trump's "Advisory Commission on Election Integrity" was just successfully sued by 1 of 4 Democratic members of 11 total members for hiding its activities from view + refusing to share documents.
Trump had falsely claimed millions of illegal voters cost him the popular vote in 2016 and the committee began it's "work."
Many say Trump's panel is politically motivated. Back in June, states believed Trump/Pence were actually launching "voter suppression" efforts.
What's the probability of that?
2
David, Perhaps you could start keeping a scoreboard that tracks the probability of Trump suspending the 2018 midterm elections. Most people simply assume that "it can't happen here" and so would assign the odds at just about zero. But the probability is surely far higher.
Trump knows what he has done, which is why he's so scared of Mueller, the dossier and his own tax returns. I for one still have a hard time believing that Benedict Donald himself wasn't in the room during that infamous Trump Tower meeting in June, 2016 (after all, it's been reported that he was in the building at the time).
So Trump isn't so much worried about impeachment--he may be forced out of office in disgrace but will have made himself far richer in the process. No, the stakes are much higher. The statutory penalty for high treason is death. Trump is not going to hang, but the law mandates a MINIMUM 5 year jail sentence. Dying in prison is not what Trump has in mind.
Mueller is almost certainly building the case for treason. That's why Trump will have to fire him, setting off a storm of protest. With this sycophantic Republican congress, don't hold your breath waiting for impeachment proceedings to begin.
The firing of Mueller will likely lead to a democratic landslide in the 2018 midterms--if they're allowed to happen. Trump knows he'll be impeached and then tried for treason. Why would he allow this to happen?
Maybe the only way to prevent this from happening is to think that it can.
5
People have discounted outlying probabilities in all areas of life, including a rather famous meltdown of a hedge fund created by Nobel laureates that discounted several black swan events. Then when it happens we try to rationalize our previous behavior of ignoring the possibility that it might happen.
You should always be cognizant of this in the investment world, particularly when a recent study says 51 % of the population thinks that now is the time to be invested in the stock market....be careful
3
We have to have the intelligence to tell the difference between a story and facts. The Republican Rich Royalists have had the better story for the past 4 decades. Despite the glaring opposing facts, the story line the RRR has broadcast has won out.
However, when the story line becomes so obviously false, even the blind can see the hand writing on the wall, then the revolution will turn the tide.
Vote the RRR out of office in 2018 and bring freedom back to the populace and prison to the white collar criminals. Vote in 2018 and throw the bums out.
2
And don't forget that deep core gut feeling. Data is just one part, but I see increasing reliance on numbers that can often be manipulated to sway an opinion one way or another. Listen to your core and do the right thing for everyone, not just you.
As a statistics/actuarial professional, I applaud the discussion of probability in the context of policy. However, do not lose sight of an all important part of our public discourse: lies.
Lies create confusion, hide truths, distort all our predictions. Self serving liars have a single minded focus, pulling off the con. The rest of us search for the truth and do the best we can. I think the tobacco industry set the standard of ‘selling doubt’ and creating just enough confusion to push back settled science. Today fossil fuel companies, pharmaceutical companies and republicans are following in their footsteps.
5
Mr. Leonhardt, one way to deal with the "abstraction" of the probability quotient is to play it out further: we all know that people actually do get cancer; if there is a probability that five out of a thousand persons will get cancer of a certain sort, then that means that you can be almost certain that about 800,000 to 1600000 WILL get cancer (depending on sex-linked or not). It might be a lot easier to imagine for the reader to understand that there is a real chance that someone he/she knows WILL get that cancer. Then the story might be more impactful also.
1
Understanding probability is usually more important than calculus in high school. If you can get your kids to take AP Probability and Statistics, that is a great investment, as these topics apply to everyday life, for everyone.
https://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_ed...
And a crucial factor to consider is error analysis. Random (+/-) errors can be accounted for in an experiment and can be described mathematically. Systematic errors are the killers. You don’t even know they are there, and they skew the data in unpredictable ways. It was the systematic errors in the 2016 election that surprised everyone when the results came in, “defying” the polls.
The good news is that we can stack the deck in our favor by preparing well. For future elections, for example, what can we do?
Something like the Mueller investigation – pretty much we can only watch. But we can use good persuasion skills to sway voters, we can ensure they are registered to vote and that they cast their ballots, and we can engage in peaceful protests.
We can also do a good job informing voters for the next elections. That’s where local and national media will play crucial roles. It is time to stop complaining, and time to start doing.
Here in Arizona, we potentially have two U.S. Senate seats up for grabs. We should see ample discussions concerning the candidates, starting right now.
We need to get the systematics working in our favor. That’s always the key.
1
The commentary is perhaps valid re communicating risk: a picture is worth a thousand words. However, it's confused about "probabilities." Someone's subjective feeling of certainty about a future event is not the same as the odds of drawing an ace. Even the example of a girl being 5'9" is problematic. If you have information, for example the parents' heights (and why wouldn't you?), then the "random baby" concept is meaningless. Predictions are not so much about probabilities, they're about the quality of the information available now. GIGO: garbage in, garbage out.
The Times should avoid pseudo-probabilities about the future and instead focus on providing accurate factual information about current reality, including recent history. Thus, with respect to the election, instead of telling us a thousand times that Hillary Clinton was a "qualified" leader it would have been informative to compare her actual record on major issues (Iraq War, civil rights, bank deregulation, etc.) to that of other candidates in the primaries.
Fine column with an understandably misleading headline and fine comments, all 24 of them, since those with possible errors elicit good replies. Leonhardt succeeds in creating a comment column at its best, a genuine discussion in real time not restricted to Verifieds.
As more than one comment writer suggests, teach the kind of knowledge discussed here, more often and better. But remember that in an America in which serious science has no place as long as the current administration reigns, those who will teach the courses we envisage will have to choose their case studies carefully. I learned in teaching about flood and earthquake risk that it was hard even for many to grasp that if a so-called 100 year flood occurred that did not mean that such a flood could not occur again until 100 years had passed. Guess Texas knows that now but will this change teaching in Texas? Are you kidding?
Here questions to comment readers, questions based on my comment obsessions.
Based on the past 5 years of columns referring to renewable energy what is the probability that any one of these terms will appear in 2018: solar, wind, heat pump, waste-to-energy, ground-source geothermal. For data search for each.
Same for the occurrence of a presentation of the bearing of genome research on belief in black race, white race in NYT Race/Related, Conversations about race, columns with race in the headline. "Not likely"
Only-NeverInSweden.blogspot.com
1
Season's greetings to you, and wishes for peace on earth, David Leonhardt. Those of us who are living life day by day (and have lived it in America since the 1930s) never think of probabilities or what journalists "were wrong about this year". What will be will be. The chips will fall where they may, but hey! the 2016 Election (which changed our world for the worse, alas) is not an event we can "do over". Not a Mulligan!
GIGO
Garbage In, Garbage Out
What was the statistical database that yielded the Clinton win estimate of 72 or 85%?
Was it based on a relevant data set?
How were the uncertainties of yet to come possible events accounted for?
etc.
When I think of the 2016 election it is abundantly clear that a database consisting of nationwide voting sentiment is completely irrelevant. The relevant data is the state by state data, translated into electoral college votes. Is that how the analysis was done?
GIGO
1
So what WERE you wrong about? Not the probabilities, but only that people can comprehend what they mean. People have been saying "See? The polls are worthless. They were wrong. Trump is President, not Hillary!" (usually followed by some derogatory term for her).
But, in fact, the polls weren't "wrong", they were misunderstood. They said Clinton would win the popular vote by 4%, and she got a 2.5% edge, well within the margin of error. The tipping point in Michigan, a state with nearly 5 million votes, was 11,000, and half of that, 5,500 would have flipped it for her--barely a 1/10th of one percent.
When I turned 18, one of the last years for the draft lottery numbers, in the early 70's, there were 365 numbers, and the odds said I should be in the range from about 125 to 210....my number was 25! What were the odds? 1 in 365! Luckily, before they drafted me out of college to go to a war I vehemently opposed (and still think was a disastrous error), the draft ended.
The adage "Figures don't lie, but liars figure!" needs to be remembered, as we see a White House and Congress that is so distorting both the figures themselves and the inferences that can be made from them. We KNOW they are lying because Trump told us so: He PROMISED he was going to raise taxes on the wealthy, but just this weekend congratulated his rich guests "You all just got a lot richer!"
America as we know it, was lost on Nov 8, 2016 to a crook & would-be dictator. Now we must fight to get it back.
3
I'm surprised that Leonhardt tries to explain probability without writing about expected value. Probability is useless as a decision tool without also knowing the costs and benefits of the different outcomes you are evaluating. For example, the you can't rationally choose between a bet with a 90% chance of winning and one with a 10% chance of winning, unless you also know how much each bet will win. If the 90% bet returns $1,000 (expected value $900) and the 10% bet returns $50,000 (expected value $5,000) it almost always makes sense to pick the 10% bet.
Dumbing things down to "you need a story" is a disservice to your readers. Even people who hate math can understand the power of using expected value to make decisions that involve costs and benefits.
Instead of saying Hillary had a 75% chance of winning, reports should have said she was about as likely to lose as flipping two fair coins and having them both come up heads, or as rolling a 1 on a fair die. People instinctively understand that two heads in a row happens sometimes, and isn't even all that unlikely.
Start going into Bayesian vs frequentist and you'll lose everyone.
oh, come on, those election predictions that said Hillary had a 72% or 85% chance of winning were wrong, those statisticians need to to go back to the drawing boards. Weren't there many states where she was ahead 3% and the margin of error was 3%? The pollsters were right on most states, wrong on just a few, but those few went for Trump. What were the chances of that happening? 15 to 28% according to the political statisticians. Maybe that would have been true if we were dealing with red and white balls in a jar, but when dealing with people, that should have been doubled to a 30% to 56% chance of error.
Or they did not factor in the Russians. Garbage in, garbage out.
Don't get fooled again.
"Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
Well, President Obama certainly didn't acting as if Trump's odds were zero.
As ABC news put it, "As he barnstorms swing states in the closing days of the 2016 race, President Obama is forging an unprecedented final campaign for an outgoing incumbent president not seen in the modern age -- and a move that could help tip the scale in Hillary Clinton's favor. " http://abcn.ws/2eAzARI
1
Too little, too late. The Mueller investigation should have started long before the election, not after.
You've said what probability isn't, but you doe't say what it is.
How about just skip the reporting of probabilities? Report what is known and what is not known.
2
As you almost point out, we humans understand the world in stories. And we can't hold two stories in our minds at the same time.
It might not be that people "didn't understand the statistics" on the election. It might simply be that we could not believe that a huge number our fellow citizens would be taken by an ignorant, incompetent, immoral con man.
When people expect every story to be told in the space of a bumper sticker, probability is far too technical.
3
David, give yourself some credit.
Because, who would ever thought that 46% of our citizens were intellectually shoddy and morally bankrupt?
I believe there's an old saying that goes "Figures don't lie but liars can figure."
1
we born and we die, between these two the life we are going to live up to us, faith is good but today lots of countries leaders do their work hiding behind faith,faiths are hear make us a good human been, till we see the all humans same, l mean black, white, Muslims, Christians , Jews so on so forth our world is in trouble, Trump is the president because he was elected now if we do not like it next time don't but a daily attect is not good for USA, and again if l may this goes every part our life life is good the people makes it bad take care l wish a healthy and happy 2018
What I was wrong about this year:
Well, it took me about 15 minutes to understand that Trump is a fool, a knave and a bozo capable of ruining this country. A tragic mistake on my part, because I had just been about to embark on a massive fundraising campaign on behalf of Alfred E. Neumann, a man of intelligence, impeccable character and humor who would have mopped the floor with Trump and made a fine President.
Mr. “What, me worry?” vs. Mr. “I’ll make you worry.” Ah, what a loss!
3
http://www.madmagazine.com/taxonomy/term/29391/all/feed
1
Many TV weathercasters do not understand the National Weather Service's "Probability of Precipitation" ("POP").
https://www.weather.gov/ffc/pop
1
David, you were wrong about a lot more than this. Whatever it is.
1
That stories are a requirement for bringing understanding is not a recent communications breakthrough. Jesus was a storyteller. And, storytelling skill development proliferates in successful businesses. If that's a revelation at the New York Times, shame on the Times. Perhaps too many describers of the probability of an event have not acquired sufficient statistics competencies to offer stories that are both attention keeping and include the actual meaning of probability.
Leonhardt's example of Obama administration officials' rounding Trump’s victory odds down to almost zero is a good start of describing the problem. But pointing out that sort of intellectual laziness (smugness?) without offering the needed story is an example of the failure. As one regularly used example, every day the FAA's Air Traffic Organization provides service to more than 42,000 flights and 2.5 million airline passengers. If there were "only" a 10% predicted failure rate in safe conclusions of those flights, 4,200 would have concluded with injuries, at least some calamitous.. That’s a story that can be understood. And, it also shows that a low probability of any occurrence doesn't suggest what won't happen, but what will happen and with what frequency.
Of course, there's a low probability of another identical Clinton vs.Trump election. But, there’ll be enough close comparables that should forever drive out complacency. And, the Times may need acquire additional statistical storytelling competency
6
"...Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero...
This is so frighteningly Kafkaesque, it's hard to know where to begin...
Along a similar line, would they treat a possible mass terror event less seriously - if it targeted a Ted Nugent concert, vs a U2 concert???
But - back to your non sequitur...
If these folks - even as improperly focused, as they were, on handicapping the odds of the 2016 presidential election, and letting that influence their ostensibly non-partisan worldview - basically blew it...
With that - why should we accord them any presumption of integrity or competence, on anything else they deign to weigh in on...
e.g. Syria, Afghanistan, North Korea, China, Russia, etc...
Or - broadening the aperture - climate change or US GDP growth...
1
What is obvious is that the MSM uses polling to sway opinions, not determine what opinions are.
The NYT proclaiming that Hillary had a 95% chance of wining was not based on big data but big hope.
"...might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
Actually, the Democrats knew the probability of Russian collusion and interference in our election was zero because the Democrats were the ones that paid for the fake Russian dossier that dreamed up those claims.
2
We all use probability. Wisely, we couple it with consideration of outcome from our choices. Consider: .01% probability of being hit by a truck on the way to the grocery store. On the other hand, there is a 0% probability we will survive if we don’t eat. We weigh the probabilities and outcomes and go to the store.
5
Probabilities are almost always approximate estimates. The data they are based on can be of reasonable validity, such as when polling likely voters, or less so, as when estimating the probability of war. In both cases the probabilities are only estimates based on assumptions.
1
In addition to the problems of statistics in effective decision making, there is the issue of ego—not wanting to be seen as wrong—particularly at high levels where concerns about one's reputation are magnified (cf, Halberstam's The Best and the Brightest, Sorensen's Decision-Making in the White House, and LBJ's increasing disastrous involvement in Vietnam).
At such levels there is also a susceptibility to the formation of self-reinforcing bubbles that are resistant to fresh perspectives from those who have not engaged in the self-promotion, back-slapping and conforming that are often part of process of rising to the top, and the drive for power.
14
Kahneman was horrified not because the official approximated 0.1 to 0, but because one should not lightly pursue a strategy which increases the probability of catastrophe by 10%. The only way someone would take a flight that has a 10% probability of crashing is if it were the only way to avoid a 90% probability of dying. It's also why rational people buy insurance.
16
The worst case of numerical regret must go to the Princeton neuroscientist and ace electoral analyst Samuel Wang. Wang prediction record for the previous three election cycles was virtually 100 percent and he was absolutely sure that Trump was a sure loser right up to election day. He had Trump as a loser at over 99 percent until suddenly on the day of the election he happened to give him a five percent probability. But for weeks up until the fateful event he had assured readers of his blog that this thing was foregone conclusion. It was written in the stars and in the statistical certainties he had found in the electorate. Indeed, he very accurately predicted a Clinton win in the popular vote by a little over 2 percent. Unfortunately, he also saw her winning the electoral college a little over 300 electoral votes. Pennsylvania, Wisconsin, Michigan and Florida were supposed to drop into Clinton's column albeit narrowly. But it didn't happen.
His rival, Nate Silver, also predicted the likelihood of a Clinton victory but he still gave Trump a real chance of pulling off an upset. Trump had 35 percent chance of victory according to Silver's somewhat less quantitative approach to electoral analysis.
And that was that. We now live in the awful real world of a Trump presidency. It wasn't Samuel Wang's fault, he just got it all wrong. And how painful that is.
8
How about the coin was weighted by the Russians and we did not know it. Just how would factoring in hacking by the Russians have changed the probabilities? I'm certain there are research models out there now studying the effects of various maniupulations on the predicted outcomes.
1
It is difficult even to state what is meant by probability in a convincing way, especially probability associated with single events. Bayesians, for example, define probability simply as 'degree of belief.' So it is hard to say that Sam Wang's probability was "wrong" in a meaningful way. But he clearly could have done a better job in assessing the uncertainties surrounding polling. And it seems fair to say that he is just a tiny bit responsible for Trump's election by suggesting to his readers that, because the likelihood of a Clinton victory was so high, their resources and energy were best devoted to other (non-presidential) races.
The point of the article is that people will not get it through their heads that statistics, no matter how good, DO NOT PREDICT: they tell you probabilities, and we add on the AHA! part.
Wang got it right: Trump's election was a very low-probability event, like the time a flipped a nickel and it landed--and stayed--balanced on its rim.
1
I read through the Intergovernmental Report on Climate Change for policy makers. It expresses all its conclusions in terms of probabilities. This works well for scientists and scientific discussions. It’s not very effective for the polemics of politics. On the other hand, I remember that around 1935 or so someone asked Einstein about the possibility of striking the particles in the nucleus of an atom by bombarding it with neutrons or protons. He didn’t respond with the probability. Rather, he responded that it would be like hunting ducks by shooting a shotgun straight into the air in a place where there were very few ducks. Later, when the chain reaction was discovered, he responded, “I never thought of that.” Einstein was said to have on the wall of his office a poster with the statement, “Not everything that counts can be counted. Not everything that can be counted counts.” The obsession with numbers always brings me back to Robert McNamara and the way he calculated what was to be our victory in Vietnam. His obsession with quantification and statistics has since been seen to be a form of insanity. I’m not impressed with probabilities. I’m not impressed with Kahneman.
7
Those chain reactions are also probabilistic events, as is your commuting to work and arriving safely.
But Einstein also said "God doesn't play dice with the universe." But in fact God, if he exists, probably does.
This is an important column brilliantly presented particularly the link on how to effectively handle the fear laden risk of cancer. Thank you Mr. Leonhardt, I am looking forward to your work addressing the difficult issues ahead.
6
Probabilities require a logical mindset and the ability to be comfortable with ambiguity. Most people prefer simple straight answers which is why they struggle with probabilities.
I wonder where we might be with the Russian collusion investigation had President Obama ignored the naysayers and issued a warning to the American people that Russia was attempting to interfere in our election. Would that have been enough to prompt the electoral college to recognize that Trump was unfit for office based on his previous relationship with the Russia and perhaps it would be best to follow the will of the people. Sadly we'll never know if a well timed warning would have changed our current situation. Some lessons must be learned the hard way.
6
It's probably important to remember that in November 2016 there WASN'T a national election but 55 separate and simultaneous elections: one in each of 50 separate states, the District of Columbia, Puerto Rico, Guam, and the Virgin and Marianas Islands. According to the FBI, some (maybe 20) of these incurred some sort of access by foreign operatives, including, but not exclusively, Russian ones. Russian (and possibly other) use of the internet to brainwash voters and possibly skew voting patterns clearly was pandemic, of course.
I've been wondering what specific Russian espionage activities caused the Obama Administration to close two Russian diplomatic facilities and expel numerous intelligence operatives from the Russian Embassy and San Francisco consulate. Might it have been internet manipulation? (Whatever it was, the Russian response early in 2017 was draconian.)
1
true. I tore clinton apart on social media for all her sins, for monopolizing the Democrat party apparatus to beat Bernie, for not being the best candidate to beat trump (Bernie), but I did that because I was confident she would beat trump anyway, 90% probability. Well, I wouldn't be the first general to underestimate the enemy. So did Clinton.
6
And that is what Leonhardt is talking about: the misread of the numbers, which did indeed get a lot of leftists to believe, falsely, that they had the room to say whatever they liked, and there would be no consequences.
By the way, that's not what freedom of speech in politics implies. It implies that you have a responsibility to speak up, and damn the arriving torpedoes.
One hopes that Trump will have taught everybody that this ain't a game.
Clinton beat Trump by 3M votes. That is how the country voted nationally. She was defeated by the Electoral College: a gerrymandered 77,000 votes controlled by corrupt Southern governors. If we ever have a Democratic Congress again, we need to march until they are forced to repeal the Electoral College. The purpose it served, to bring the South into the union by giving them votes they had not earned, is no longer relevant. In fact, the EC has corrupted and distorted our government.
It doesn't seem to me that the big story of 2017 was that most pundits called the election wrong. Everyone makes incorrect predictions. Rather, it was that some 63,850,000 of their fellow citizens called it wrong when they voted.
16
I agree that people often round probabilities to 0% or 100% in their heads. But they are better at understanding the risks when they can imagine what would cause the less likely outcome, and when they are strongly impacted.
If someone has an 85% chance of surviving surgery, they will be scared. They understand that people die all the time from surgery and most of us have watched it on TV. Or imagine being told you have an 85% chance of not dying in a car crash today. Who would get in the car? We've all seen fatal car crashes on the news and imagined the causes and how the victim felt.
For an election, people have trouble imagining the esoteric causes of the less likely outcome happen - exactly how the electoral college could skew the popular vote, the distribution of polling places, availability of early voting could. And they cannot imagine how the result transformed our world and directly impacted them: in my case, obsessively following the news, going to rallies, reading the history and psychology of tyrants, the constitutional framework, legal approaches to stopping actions of this administration, and greater financial support for political and environmental groups and reputable news organizations.
The press should have done a better job explaining the causes and personal and global impacts of the less likely outcome.
5
I dunno what press you watched, but the ones I watched, listened to, read, told me precisely what Trump is, and precisely what the consequences would be like.
1
The human mind is an inference-making device, but not a very good one: "I have a high cholesterol level, but love vanilla ice cream with chocolate sauce. So I'm likely to have a heart attack. But suppose heart attacks are mainly caused by inflammation of the coronary arteries due to bacteria in my blood. So maybe I should forget about cholesterol and ice cream and focus on brushing and flossing my teeth and making regular visits to my excellent dentist.
The point is an old one made by the Reverend Thomas Bayes: What are your prior beliefs? You are right, Mr. Leonhardt. If President Obama didn't believe with such a high degree of certainly that Hillary Clinton would win, he might have dared offending Trump and the Republicans by exposing the Russian treachery at a time when it might have made a difference. It is too bad he didn't have a statistical consulted that he trusted.
8
Every single day prior to the election, John King, the political analyst at CNN would say the it was likely that Hillary would win the election. However, he would also give 3 scenarios whereby if Mr. Trump won a combination of different States, the he could, indeed, win the election.
The reality was that almost everyone was dismissive of any analysis that showed that Mr. Trump COULD win. Everyone, liberals and conservatives, wanted to hear only the analysis that they wanted to hear....Everything else was discounted. We only look at information that supports our beliefs which is one reason that Fox News is so important for its viewers.
9
David Leonhardt's OP-ED read as a lesson in statistics. Was the high 'probability' that H. Clinton would be elected president the only reason Obama neglected to trumpet Russia's interference in our election? Were there no foreign policy issues also responsible for his administration's inaction? In addition to the belief that Hillary would win, might there have been additional reasons for Obama's hesitancy? Now, with Trump as president, Russia clearly has the upper hand, which is exactly what Putin worked toward. While Leonhardt has warned us of the misuses of probability, he appears guilty of basing his final analysis on it. Withal, David provided us with a good story/lesson; low probability doesn't mean that it won't happen and high probability doesn't mean that it will. Obama misuse of probability, according to Leonhardt, wasn't the only one at fault, the democratic party and those of us that didn't vote were also at fault. In the final analysis, here we are with the terrifying reality of Trump.
4
"THose of us who did not vote," were very much at fault, and still are.
1
And how about the lotteries?
Everyone knows the chances of winning are ridiculously small - a million to one or less.
But someone actually wins every one.
9
Not always. That’s how jackpots grow so large.
3
But ultimately - the concept stands.
1
And the conclusion is “Why not me?”, right? It’s the conclusion that’s flawed.
With the USA ranking at the bottom of Industrialized nations in math, science, and education, who is surprised that people confuse the probability of the event with outcome. Add the local and national weather "forecasting" to this mix and who is surprised that the citizens of this country cannot use this data correctly. If the weatherperson (why they exist other than telling us what happened, I have no idea. After all the rest of the program is reporting on the facts of what occurred or what is occurring with no outcome prediction) predicts 20% of showers, 80% of not, and it rains, they were wrong about it raining out my picnic. No they just said the probability is for a nonrain event.
No wonder Las Vegas keeps clicking along and building bigger and bigger casinos. Or we have a public that can now no longer wait for the end of the book or movie
2
Actually, weather predictions are quite accurate. People just like the myth that they’re not. It gives them something to complain about.
Often heard in Christian circles, 'Only believe'. Are statisticians feeling the chill of 'buyers remorse'? Are statisticians letting down big science? Confession might be good for the soul. Its not just about a vote, money might be on the line. Are we going to be seeing more stories, maybe parables? Might be unpredictable, unlike the death rate which is still one apiece.
Gigerenzer's research shows that most people are just better at understanding so-called natural frequencies- such as fhe quoted example: 77 people out of 1000 will get X camcer, and 5 will die (one out of each 15 diagnosed).
The "provability of one event" is in another category and very few people can understand rare (N small or N=1) events: If you want to understand Trump do you treat him as you would treat a single toss of the dice among 45 tosses? (No). Some situations force a nuanced understanding of probability when even is singular. Also, in many cases, even if the probability can be expressed in frequencies, what matters is not the probability but, rather, a loss or utility function. If you are Janet Yellen what matters is not jus if policy decision A has 10 percent more chance to suceed compared to B, but also if whether A or B are more likely to help or damage the economy: Trump may be an outlier but he seems to be the proverbial black swan, which means we'll be picking up pieces for many years.
2
Steven King couldn't come up with a storyline more nightmarish then the one we've been living through this year. The story of this year has no heroes, no comic relief and no happy ending. This "Mister Smith Blows Up Washington" scenario wouldn't go down easy in any narrative or mathematical form. The only thing I'm sure sure of is that there is a 100% chance that I will wake up tomorrow appalled, because I have been everyday since Nov. 8 2016. Merry Christmas Mister Putin. Not only did you get the Presidency you asked for but the Republicans have thrown in the Congress and the Judiciary as well.
9
While we're at it, we could use some additional basic numerical literacy. I witness the lack of it all the time when people talk about government spending and of tens of millions or hundreds of millions of dollars. Those figures certainly sound hefty to an individual, but compared to the 3.8 trillion federal budget they are microscopic.
Make a quick guess, what is 1% of the federal budget? Answer: 38 billion, which can also be thought of as 38 thousand million. So really, in news reports about government spending, my ears barely register millions, and they only begin to perk up at the tens of billions.
Remember, a billion is a thousand million, a trillion is a thousand billion.
4
This is a great explanation for the Pavlovian response seen from right wing commenters whenever the term "poll" appears in discussion, say discussion of Trump's abysmal approval ratings - "polls are useless because they said Hillary would win."
1
The refinement of probablitiy theory which you attempt here is lacking. The man you cite, Danny Kahneman, in his bestseller, "Thinking, Fast and Slow," himself cites the guru of probability and the author of "The Black Swan." Kahneman says "overconfidence is fed by the illusory certainty of hindsight. My views on this topic have been influenced by Nassim Taleb...I hope for watercooler conversations that intelligently explore the lessons that can be learned from the past while resisting the lure of hindsight and the illusion of certainty."
There are some domains where classical probability can provide useful insights, usually those closest to the physical world. For example, look at a stadium full of 50,000 persons. If I bring one more person into that stadium, even the heaviest person in the world, the average weight of a person in the stadium will not vary by more than a negligible amount. If I consider the average wealth of the same 50,000 persons and bring Jeff Bezos into the stadium the average wealth will vary by thousands of percent. The weight domain is susceptible to probabilistic forecasting. The wealth domain is susceptible to Black Swan type events. Almost all historical, sociological and economic forecasting is susceptible to Black Swan events. This vast difference is usually ignored. In my view, some things are just not susceptible to probabilistic forecasting, but they are susceptible as Kaheman said, to the illusory certainty of hindsight.
2
I, for one, am not inclined to give the pollsters much wiggle room when they get so cocksure of themselves. There was one 2016 poll that promised to be the most accurate ever, combining the pre-election day polls with real-time exit polling. It had Clinton winning every swing state. And the media has learned nothing, continuing to treat these polls as gospel. I would certainly be more forgiving of the polls' lack of certainty if only the pundits and pollsters would do the same. Sadly, they have become addicted to them.
1
Merry Christmas! Human beings are not hard wired to understand probabilities, but tend to focus on rare events that are perceived to be harmful or favorable (i.e., flying on a plane that crashes, winning the lottery, etc.)
Some people, however, appear to be hard-wired to crave certainty (100% likely or 0% likely) in their lives and develop an internal compass where every decision or event must be binary (1 or 0, right or wrong, black or white, etc.). While this simplifies the need for critical thinking, it make life very challenging (I think).
Senator Flake's remarks, as he approaches the end of his career in the Senate, are a clear warning bell for the GOP. The dilemma of the GOP reminds me of how some publicly traded corporations feel compelled to yield short-term results (i.e., win elections, support the "base" of angry older white men) to appease VIP shareholders (i.e., wealthy GOP donors).
Instead of looking strategically at long-term investments or new business developments over a 5-10 year horizon (i.e., diversify the GOP's voter base) , the dying corporation exploits its old business model until it declares bankruptcy (or the CEO is forced to retire). The certainty of old formulas that seem to work (as flawed as they are for winning elections in the long-run) may be outweighing the dire need for the GOP to develop new strategies.
3
If the all to human tendency to round up or down wasn't enough to delude the math illiterate, add the concepts of complexity, and chaos (both large scale and small) and the most educated and naturally adept, without a really good grasp of how mathematics works beyond the simple arithmatic we need for our daily lives, is likely to simply say that 'it can't happen', or worse 'it will definitely happen'. In the mean time; expect the unexpected.
2
Classical risk analysis used by casualty insurers weighs the probability of an event happening and the cost in damages of a payout if it does happen. That type of analysis also considers the cost, in case there is a dispute on causation, of litigating the issue versus the cost of paying out a higher figure to the claimant to realize a savings on litigation expenses.
This is all very logical when dealing with very similar risks dozens or hundreds of time each year. David Leonhardt is correct that the ballgame changes when you look at one-time events like an election or a war.
There are two very different enemies: recklessness and complacency.
Donald Trump appeared reckless, but he had nothing to lose, because few expected him to win. He ran on a shoestring budget, and primary victories generated a surge of contributions. After Trump won the nomination, the rest was gravy. The publicity earned for his businesses early on was enough to make the process worth it.
Hillary Clinton had the election to lose, and that created pressure. She chose – or people around her chose – to accept that her lead made winning a virtual certainty. She became as complacent as Trump was aggressive.
The mistake made by David Leonhardt in assessing the relative chances of Clinton and Trump was made by a majority of pundits, whether or not they have Mr. Leonhardt’s honesty in admitting it now.
1
A good explanation by Leonhardt of probabilities. But then he closes with this doozy of a statement:
"The rise of big data means that probabilities are becoming a larger part of life. And our misunderstandings have real costs. Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero."
It continues to gall me that there is no clarity on whether or not our government under Obama saw "meddling" by the Russians in the 2016 election. If they did see evidence, they are as egregiously at fault, if not more so, as the Trump campaign since the government then suppressed information the voters should have been told about. If our government did not see proof of Russian interference, then this whole Mueller investigation is as big a witch hunt as Ken Starr's hounding of President Clinton.
3
Well, as far as pundits go, I recall reading that Clinton had an 85% probability of winning the election, right up to the election itself. It is very possible that many Clinton voters didn't vote because it was in the bag.
Remember who created that probability? Nope, but it has had a major effect on all. That pundit owes us an explanation.
1
Sense About Science, http://senseaboutscienceusa.org/about/, is available to help. Their "mission is to improve communication, transparency, and the use of evidence in the sciences."
Attributed to many, it remains true nonetheless, "He uses statistics as a drunken man uses lampposts – for support rather than for illumination."
Never lose sight of the fact that probability theory arose from the study of games of chance by, for example, Pascal and de Fermat.
The author, and most news media, are (deliberately) not talking about the elephant in the room. Most probabilities are based on polling results (either of the voting kind, or reporting kind [e.g. collecting intelligence reports - or to use another example, where a business decision relies on inputs from experts and/or marketing polls]). But most polls are inaccurate - some wildly so (e.g. the 2016 predicted Clinton win, or the 1948 predicted Dewey win). And probably the other kinds of polls (marketing surveys, intelligence analyses, etc) are equally inaccurate - for the same reason: people lie - to themselves and to the pollsters. People don't often know their own minds, and on Monday will choose option (A) and on Tuesday will choose option (B).
Probabilities are only half (or less than half) of the story. It is the payoff that really matters. At the roulette wheel these are easy to calculate: On a wheel with 0 and 00, the odds against a single number are 37:1. The payoff if you win a dollar bet on that number is $35. So on average (over many spins) you will lose 2 cents on every play. That number is called the "expectation" --- it is the average win or loss over many plays --- if negative you will always come up short if you play long enough. (That is why, even without cheating, a casino always wins over the longer run --- which makes it a mystery how trump managed to go broke in AC.) If the probability of war is 10% (which seems tolerable) you must multiply that fraction by the cost of war as opposed to the benefit of keeping the status quo.
2
If one believes in justice and logic over partisan politics here's one future event with high probability: As Mueller gets right up to the door of the Oval Office, Trump will fire him and force the hand of a GOP controlled Congress to proceed with impeachment hearings.
Don't blame prediction errors on probability calculations, blame the errors on the the data, the poll taking. For elections the poll takers ask people for whom are they are going to vote, but people change their minds and people don't always tell the truth. I would be curious to see the data that was used to predict that the Falcons had a 99% chance of winning.
"I think part of the answer lies with Kahneman’s insight: Human beings need a story."
Or this is another way of saying that when you deal with human beings, they do not always function according to the numbers.
As an officer in the psychology unit of the IDF, Kahaneman had also been asked to evaluate performance of officer candidates in officer training re their future command, and determined that how one functioned in the course would have little bearing on how one functioned as an officer during combat. Human beings, people (under pressure), trumped the numbers.
Life is not a dice roll and the sum total of probabilities.
1
Kahneman himself has acknowledged that merely educating people on the cognitive biases inherent in thought and decision making has done little to minimize or eradicate those biases. So an integrative narrative remains paramount to our functionality as a species. Hence, all that is left for us mere mortals to grapple with is how much we are fooling ourselves about how much we are fooling ourselves.
3
Instead of lamenting that 300 million Americans do not understand statistics and probabilities, we need to admit the real problem is with fancy college degrees and 5-6 figure salaries our journalist class has been unable to inform the citizenry of what is true and what is made up. That is the sum of it. All of this hand-wringing and pseudo analysis is pointless. If we spent so much on healthcare and had patients dying of the common cold by the thousands we will not be talking about probabilities, we will be running investigations into what and who all failed.
1
a probability that i am not looking forward to? the probability that democrats will not run a convincing candidate in 2020 and we will get 4 more years of disaster. with absolutely no data whatsoever? i attribute a 75% chance that this will happen.
This article makes me think of two people: Robert McNamara (Secretary of Defense under Kennedy and Johnson) and Nassim Nicholas Taleb (author of "The Black Swan: The Impact of the Highly Improbable").
McNamara was trained in statistical quality control (SQC) at Harvard Business School. He was highly regarded as a "whiz kid" and made significant contributions to the Army war effort during World War 2. He rose to become President of the Ford Motor Company where he was credited with reversing the declining fortunes of that company using SQC. At Defense, he implemented SQC to improve decision making. This led him to devise metrics for the Vietnam war, including enemy "body counts" and "kill ratios." These metrics appeared to show that America was decisively winning the war. But, despite more and more troops, money, and material; favorable metrics; and optimistic reports from Gen. Westmorland, something was amiss. McNamara went to Vietnam several times and eventually concluded that the metrics did not reflect the true status of the war effort and that the chances of winning were actually unfavorable. When he reported this to LBJ he was promptly fired.
Taleb taught us that just because the probability of a rare event occurring is very low, the fact that it is not zero means that that event could still occur and with devastating consequences. If you cannot tolerate the downside of an occurrence of a rare event, you are foolish to bet heavily against it, even with favorable odds.
3
Probabilities are difficult to deal with, not to grasp. You are partially right about the Obama admin rounding up the probability of Trump's victory to zero, but that was not mishandling probabilities, that was a full misreading of reality. Russia may have pushed the edge. But the 46% that voted for Palin was always there and still there. I hope the dems play to win, not to make smart points. But what is the probability that the dems stop misreading reality?
1
Oh, still cannot come to grips with the loss and inventing new ridiculous explanations? The polls that were showing 87% of win for HRC were skewed 10-15% in favor of Dem participants. DJT won in a landslide - 56.9% to 43.1%.
Of course even US national soccer team can accidentally beat Germany - but not 5:0. Nothing happened because of people's misunderstanding. Everybody understands what 87% means, with a story or without. Just funny to think that people who spent their whole carriers on some subject suddenly realize that the simplest and obvious basics of their field are wrong - that they promoted an apple as a very healthy fruit, and after 20 years of doing so suddenly found out that an apple is not a fruit. Please.
1
Benjamin Disraeli summarized this phenomenon a century and a half ago.
1
sportscasters who live lives on paper probablites offer a chance to see "story making" live as their predictions and predilections are overturned in front of their eyes...how many tennis fans have heard "it looks like it'll be a long day for x" who has dropped the first game of the first set at love and been broken in the second (replete with back up past performance history promising the probable disaster)...only to hear the experts back and fill as x finds footing and stroke and ultimately defeats y.
in this case the 'casters are seizing on actual evidence, however scant, and creating probabilities as a way of demonstrating their insider expertise...the affliction shared by most probability analysts and pollsters.
the investment pays off it x loses as badly as predicted, it fails when he wins.
the probability of a white christmas (happening now! btw) says that it'll happen only ten times in a hundred but it says nothing about what going to happen THIS time.
same with the die cast...chance of a snake eye or a box car are the same every time, "heads" ten times in a row still does not change the 50-50 chance of eleven or "tails."
A similar case of misusing statistics was made by Dick Cheney after 9/11. He said that a tragic event, such as a suitcase nuclear weapon brought into NYC, must be treated as a certainty even if the probability of it occurring is less than 1%. What is missing and what Chaney failed to consider is the proviso that everything stays the same, but in the real world that never happens. Things always change, and they did.
People also project trends into the future, as in "if this continues, we will all be broke or rich or dead." Well, we will all eventually be dead, but trends can be very temporal and humans can bend many curves.
1
The story I can't shake in my mind---which began on election night---is how Trump would rule as president. So far, I know from a statistical point this sounds improbable, but every detail of my story has come true.
1
And hoping that anyone with influence will take the trouble to understand the simple concept of Bayesian probability
https://en.wikipedia.org/wiki/Bayesian_probability
is a fool's errand. But it is in wide use in many fields, including the intelligence services of every country.
1
The media was tone deaf about the election. Those of us paying attention noticed the anger and saw the catastrophe that was about to happen. The media couldn't see it because it was unthinkable but it was not impossible, they couldn't see that. Probability is based on too much fact and reason and doesn't understand irrational anger and emotion.
2
I think the gravest error in the eight years of Barack Obama's presidency was that they did *not* think that Donald Trump would defeat Hillary Clinton. I think the second gravest error was the Obama administration's apparent (in retrospect that is) unconcern in deciphering Russian intentions vis-a-vis our 2016 election.
After the October 8, 2016 Access Hollywood tape went viral, I thought Trump was doomed. "Game over," I gloated to friends and relatives. What were the probabilities that, one calendar month later, the admitted grabber-in-chief would be elected? It simply wasn't supposed to happen.
If some 1's come up in 100 rolls, then what about some 100's? A Patriots fan, I watched, numb, as Atlanta rolled to a 28-3 lead with the third quarter about to end. Yet, after the overtime, I asked myself "what did I just see?" Did the Patriots roll 100's on their and Atlanta's possessions the rest of regulation and overtime? Sure seems so.
But to our disastrous 2016 election result. "Human beings need a story." But the "story" that 62-million Americans voted for meant the certain destruction of every political and societal norm that we have been accustomed to for most of our lives. I don't think it comes down to numbers, Mr. Leonhardt; it comes down to "a story."
When our national narrative flags, we conjure one up, sometimes positively, as in 2008 and 2012. But we summoned our dark side (2016) to the national colors.
You weren't wrong in 2017. We're all paying for 2016.
Until you understand why those estimates of HRC victory probability WERE wrong, you can’t seriously claim to understand probability. That she lost is not the evidence that the probability was wrong. That the calculation was fundamentally ridiculous is. The only plausible probability estimate six months out was 50/50.
Sorry David, good try but no cigar. Prior to the 2016 election, the NYTimes did have "stories" about how the election might unfold. Go to the bottom of the article: https://www.nytimes.com/interactive/2016/upshot/presidential-polls-forec... and you will see 1000 paths to victory (each path is a story after all). 31% of those paths led to a Trump victory (which is not the same thing as a 31% chance of winning because each path was not equally likely). People need to become statistically savvy - there is no substitute.
4
If the statisticians on the Times payroll had ever given Trump more than the most remote chance of victory (an NFL kicker missing a twenty eight yard field goal, for instance) his opposition would have rallied more effectively and prevented the nightmare that's come to pass. There is no way to minimize the damage those momentarily comforting, yet terribly irresponsible prognostications inflicted, and not only upon America but upon the entire world.
Oh yes. This is the real story imho. So many people, the ones that packed the Sanders rallies, in particular, (and even including President Obama) were convinced that Trump could not possibly win, by the NYT proclaiming even until the day of the election more than 80% likelihood of a Hilary win, that they didn’t bother to vote. Maybe they didn’t know the arcane rules of statistical interpretation, too bad for us, you say...then add the gerrymandered Congress, and as we have learned to our horror, democracy, our beloved country is going, going, soon gone.
2
What are the chances that a Trump administration would use statistics in a malicious way?
At least 100%.
3
This was clear on November 8, 2016. For folks who understand numerical concepts, people who don't are a total mystery. It's like speaking French. But in 2016, the continuing front page tracking of HRC's probability of winning was very misleading to many NYT readers, probably some of whom felt OK about voting for Stein or not voting as a direct result of that probability graphic. Meanwhile, to Nate Silver, it was all crystal clear. I think a lot of people conflated the percent chance of winning with the percent of those polled that said they'd vote for HRC. Just leave probability to audiences that are familiar with numerical concepts and - yeah - tell the story with words, not numbers, in the paper.
What is the probability of our surviving the next 3 years under Donald Trump? How does that probability change with or without the republicans controlling Congress? What is the probability that trump will stage a coup if he is indighted by Mueller?
1
When I once went to my Zen teacher (I practice), loaded with a HUGE problem and no simple solution, he sat there while I rambled on for ten minutes. When I finally ran out of gas, he said, "Well, either it'll happen, or it won't." And that pretty much describes almost every problem--every decision--every uncertain outcome Ive faced, before or since. While there's much to be said for planning and preparation, there's also a lot to be said for equinamity. So much--virtually all--life is beyond out ability to control. We can (hopefully) infulence things toward the better (as we define "better"), and (usually) should. Beyond that, outcomes are in the Hands of the Fates, however you may define them.
5
What I am struck by in this review is the complacency of the Clinton campaign in looking to the general polling lead while not looking to any possible weakness in the electoral vote. Ms. Clinton easily won the general vote, but that was not enough of course. Failing to look at the problem of possibly losing a Wisconsin, proved devastating.
8
Probability is like faith. It suggests an answer to things we really cannot answer that we would like to answer. It's like looking into a crystal ball to find out what's going to happen. What is going to happen most of us have no control over. We can eat healthy, exercise, wear our seat belts, etc. We can control the things we can, but often (mostly) in the end it will be what it will be.
7
It was your fate to say that.
And mine to say this.
Free will is an illusion.
1
I was always guilty of this is terms of the weather "predictions".
If they said there was a 10% chance of rain, I took to heart that it wasn't going to rain and made plans accordingly. When, inevitably, a picnic or wedding was rained out, we all decried the weather report.
I came to understand that the report works like this. That of 100 days when the conditions were the same, it rained on 10 of them. Thus a 10% chance. Still a small number, but it did - in fact - rain on 10 days with the same conditions - probably the day of my picnic.
10
Having spent a career as a research scientist using statistical analysis, the article highlights the problem of presenting scientific and mathematical probabilities to the general public. For most of the public, scientific and mathematical concepts (like probabilities and confidence intervals) are beyond their education and understanding. What is far worse are politicians and the media. A good statistical example, the 0.1 probability is seized upon as the sign of the apocalypse by a politician and ignores the 0.9 but the public, not knowing the difference, believes the politician.
9
It is good that David has joined the “I was wrong” tradition. And certainly the addition of stories could help us fallibles better understand probabilities.
However, he still maintains the very common mindset, strengthened by the heralded new Big Data age, that numbers are king.
But why should numbers be any more than one factor in judging performance, a common use, or predicting events as in this article?
They have undeserved reputations for being fully objective; speak for themselves and not subject to reasonable, but opposite interpretations; get to the core of matters, as messy “intangibles” like emotions don’t matter; and are scientific. All of these assertions can be questioned, which a focus on pure numbers doesn’t necessarily encourage. They can also be gamed (remember Viet Nam “body counts”), and can lead to unintended consequences that go against the intended system goal.
In several fields I’ve looked at, numbers are a mixed blessing. They’re often necessary and useful, but always should be viewed critically, preferably with a what-can-we-learn-here-that-we're-not-currently-seeing orientation.
So David, you're on the right track, but keep going.
8
I'm not sure any amount of explanation will get beyond the human tendency to see the odds in a certain way. In part, I suppose, how we see numbers like the 10% war probability is skewed by our nature (glass half full or half empty), our fear that the probability was 'worse,' and the company which we keep (our optimistic or pessimistic friends).
So, being a glass half-full kind of gal, if I hear that something bad has a 10% probability of happening, I think 'ok, that means there's a 90% possibility that this will not happen.' I'm then relieved (like the Israeli army guy). Even if the 10% number is statistically significant, odds are in my favor, right?
Breast cancer is mentioned. Online cardiac event risk trackers are similarly confusing. I did one recently which said I had a 6.5% chance of such an event in the next 10 years. To me, a generally healthy person, that seems like good news - 93.5% chance I won't have such a health problem seems great. The tracker, however, was instructing me to call my doctor NOW to see what could be done. That seems crazy to the average person. Hello, I have a 93.5% chance that I will be fine in this area, but someone behind this algorithm thinks this is a problem? As to stories, I'm not sure it would make a difference if you told me all about folks who fell in that 6.5%. I'd still like my odds.
10
Excellent example - which highlights how in our world of big data such information is often used by Big Healthcare and Big Pharma to push drugs, often with just the type of biased fear mongering described.
2
So much about probabilities is not understood. Take something like the odds of a plane crash, often cited as one in 11 million. Sure, that's about right if you're looking at 11 million flights. But what about that one flight that crashes? When we later find out that its pilot was crazy, or an engine was defective, or it flew into a flock of birds -- who had their own odds of being there --, we know the odds for that particular flight were never one in 11 million. Those odds are just a way of saying, "Every flight is subject to an infinite number of variables we know nothing about. All we can do is generalize."
When we talk about psychologically mediated events like elections or wars, the unreliability of describing them with odds is magnified, not only by the vastly complex and unknowable variables, but by our faulty choices of data points. Public opinion polls, for instance, are a terrible proxy for people's real desires and beliefs. They ask the wrong questions. They assume truthfulness. They assume self-knowledge. They assume the respondent actually has an opinion. They fail to take into account all the ways the poll itself shapes its own responses simply by existing, as well as by being reported. Etc., etc.
Stories really can be better. But they have to be good stories, rich in detail and history and wisdom. Telling good stories is the skill we ought to be cultivating as a corrective to the fog of squishy numbers.
65
Since David brings it up, we'll point out that without a paper audit trail to verify results, we don't actually know who won the 2016 election - it's ridiculous that we get a paper receipt for purchasing a pack of gum at the corner bodega, but vast voter constituencies get no paper ballots that can be used for vote recounts.
And for good measure, the software vendors get away with 'trust us', since they won't reveal their code; just perfect :(
More to the point, Leonhardt is correct that humans want a story, and visual aids are proven to be the best way to imprint stories on our minds, same as politicians and propagandists know we humans are very susceptible to all sorts of smoke and mirrors imagery that we see on TeeVee, believing that if we saw it with our own eyes, it's more likely to be true.
Which is why politicians just hate to be seen as perps walking in and out of legal proceedings, or as witnesses called to give public testimony to Congress - especially under oath. Great business opportunities for spinmeisters and crisis manager consultants, though.
52
Probabilities of a team making the playoffs based on their record and remaining schedule is quite different from generating a probability percentage from human perceptions and opinions. 10% chance of war? Anything not subjective about how the guy came up with that specific number?
The other thing about that is that turning human social situations into numbers and probabilities might get you in a betting line in Vegas but doesn't interest the reader wanting the details behind and around a story. I know we are now a technocratic society, but I still resist the measurability of a human soul with numbers.
6
And I resist those who generalize based on their own viewpoint, whether they’re data hawks, economic psychologists, or chaos theoreticians.
Obama administration officials, to take one example, might have treated Russian interference more seriously if they hadn’t rounded Trump’s victory odds down to almost zero....
[ What sadness. ]
73
This is an important critical review, and I am grateful to have read it since I love reading these columns through the year.
14
The 10% increase in the probability of a total catastrophe is significant; a 10% increase in the probability of light rain is trivial. So probabilities alone aren't enough. You need to also quantify costs and benefits.
There's a concept called average expected value, which is the product of the probability of an event by its value or benefit, and similarly for costs. Many real-life decisions are better when we understand this.
An example may help: After an earthquake, there is a 10% chance of a larger quake within 24 hours. The 10% risk is small enough so that you don't want to incur the cost of spending the 24 hours in a bomb shelter, but the 10% risk is large enough so that you should incur the cost of moving heavy things down from high shelves and laying in some extra water.
An introductory course in statistics would be helpful to everybody in understanding these matters. Or reading a good book about it, like Gary Smith's "Introduction to Statistical Reasoning," which is loaded with real-world examples.
193
Risk = (Chance) * (Consequences); Well watered field? or flooded basement? = 51% * 2 inches of rain.
There are three things involved in good decision-making: 1) The probability of each of the various outcomes; 2) The decisions that we can make (this is not stressed in Howard's note) and 3) The costs (or benefits) of making each of the several available decisions, given each of the possible outcomes.
The expected cost of making a decision is the sum over all possible outcomes of the probability that a particular outcome will happen, times the cost of making that decision if that outcome happens.
Simple example (my students will remember this!): If you decide to carry an umbrella, and it doesn't rain, you look like a dork. If it does rain, you stay dry. If you decide not to carry an umbrella, and it doesn't rain, you stay dry, but if it rains, you get wet. If you decide that staying dry has zero cost, and looking like a dork has one unit of cost (in some arbitrary units of embarrassment), what is the cost (in those units) of getting wet? Suppose for you it's ten times worse to get wet than to look like a dork. Suppose the report gives a 10% chance of rain. Then the expected cost of carrying the umbrella is 0.9x1+0.1x0=0.9, whereas the expected cost of going without is 0.9x0+0.1x10=1. So the expected cost of carrying the umbrella is less than that of going without, better carry the umbrella. Had the chance of rain been 5%, you'd calculate that it's better to leave the umbrella at home.
See "Smart Choices" by Hammond, Keeney and Raiffa; and "Calculated Risks" by Gigerenzer.
2
It's also helpful to define the basis for the increase. What does "increase the probability by 10%" actually mean in any instance? Does it mean to increase the probability from 10% to 20%, or does it mean actually increasing the probability by 10%, which would only raise the probability to 11%. Big difference.
1
The other thing this speaks to is that for years...centuries, really...we have treated calculus as the Holy Grail of mathematics. Except for that pesky one semester detour into Geometry all of K-12 mathematics is designed to culminate in calculus.
We would be a much more educated society if we stopped emphasizing calculus and instead focused on statistics. Sure, the future mathematicians and engineers...who are the only people who will ever use calculus, really...can still take it, but *everybody* should have a basic grounding in statistics. It's something we would use every day simply by reading the news.
346
David R overstates the role of calculus. Little of K-12 math is so designed. Does he propose that learning to add and subtract is intended to culminate in calculus? Is algebra to culminate in calculus? Of course not; both are essential to any understanding of statistics, probability, networks, computing, and more.
25
As a math teacher, I agree. The calculus is great if you are going to go into physics and generally speaking it is super cool, but most students are forced to take several semesters of algebra and trig. that are all supposed to culminate in an elective: the calculus. But most students never elect to take it. [And when I say, most students, I am referring to the vast majority of people in the US, not the prep school elite of NYC.] Most students spend years preparing for a mathematics that they will never take, let alone use. All the while I run into students who cannot do a lick of geometry. They can barely figure out the area of a rectangle. And they could not even spell statistics, let alone interpret them. Our high school mathematical education is geared for standardized tests and knee-jerk STEM genuflection. It is almost completely removed from reality. The textbooks are so bad and so expensive [and so heavy] ... you realize it is all about the Benjamins. The 11 edition of a basic algebra textbook? What has changed in basic algebra in the past... I dunno... 1000 years. Alright. Negative numbers. Of course negative numbers are what usually confuse students right out of the gate. Maybe Al Khowarizmi had it right. Do not consider the negative numbers until you have the positive ones figured out.
11
Although things are changing, the path of math through high school and college leads inexorably to calculus. “College algebra” - the biggest academic barrier to a 4-year degree in colleges and universities across the US - is Pre-Calculus, a course designed to prepare students for calculus. I say this as an academic who studied both calculus and statistics, and scratches her head at the damage we do by centering calculus over forms of quantitative literacy that would better support an informed democracy.
2
What were the chances that voters would mistrust, then reject a candidate who got $1.8 million for speeches to the same big Wall St banks that had brought about the Crash of 08?
Who then asked for the votes of millions who had been affected by that crash.
But who wouldn't reveal to voters the content of those speeches.
Who then found excuses for not restoring FDR's prudent govt banking regulations that were repealed by her husband & Gop in the '90s. Regulations which had prevented such huge crashes for generations since the Great Depression.
So, is this an example of taking the voters for granted and living in fantasy land?
The consequences? The other candidate won, and he's been exceeding even the most negative expectations every day in every way.
149
Meredith, I agree completely, what were the odds the D.N.C. would shove “their candidate” down our collective throats no matter how flawed: a year later what were the odds the candidate who sensibly promised closer relations with Russia and allowing them to help us in the situations in the M.E. thus ending a decades long Cold War would be forced into a corner to save his own hide last week and authorized the sale of lethal weapons to the Ukraine thereby escalating the war in Eastern Ukraine and seriously straining relations with Russia, who B.T.W. has been aiding us in the “War on Terror”? I would say 100% to both questions, the Office of President may have changed hands but the neo cons pulling the strings have stayed the same and will remain so until either they rule the world or take America and her “allies” down trying.
4
"exceeding even the most negative expectations"
Reminds me of the old Mickey Mantle story: asked about the 1966 Yankees he said "we've exceeded expectations, we're much worse"
10
I read the contents of Clinton's speech to Wall St. bankers et al on line. She asked them to promote more women into posts of responsibility. She said a lot more; however, she did not pander to them. She did not lie. Clinton was defeated by 26 yrs. of GOP lies and slander against her. No matter that she fought for and go medical care for First Responders; no matter that she fought for aid for Dependent Mothers with Children. No matter that she was a distinguished and much praised U.S. NY State Senator. No matter that she asked for increased funding for the defense of remote consulates and outposts and was denied that funding by a GOP Congress. Ambassador Stevens' death was blamed on Clinton, not Congress. No matter that she has put 26 yrs. of tax returns on line; Trump has hidden his tax returns which might show 250M in loans from laundered money. Trump has exceeded only the expectations of the large corporate donors who bought and paid for his Presidency. He has given them permanent tax cuts. He has allowed their lobbyists to draft legislation which the current GOP Congress will pass, much to the detriment of the bottom 99%. Any tax cuts for the middle class and working poor will sunset in 2027. Corporate tax cuts will go on forever. Gerrymandered voting districts will continue. Don't worry, Meredith. Those you most admire will remain in office.
14
Well, Hillary did win the election by getting 3 million more votes than Trump. I don’t know if the probabilities were derived on a district by district basis, which would have a smaller sampling size per district. I was an Air Force Weather Officer for 22 years. Using probabilities requires a sophisticated estimator and sophisticated recipient receiver of the information. Many users demand a yes or no answer. Contrary to popular belief, most of the weather people I worked with would do anything to avoid having to make forecasts. Mother Nature always gets the last laugh. I started in 1958 when there were no weather satellites and use of computers was just starting. Weather forecasting is much more accurate today. Eisenhower’s D-Day decision took a lot of guts.
85
People forget that Hillary beat Trump easily in the vote.
67
Clearly Hillary won the election, if you look at the votes cast and exit votes in Wisconsin. With 200 000 voters rejected and a very small number of votes given to the Republican party towards the very end of the election night, why would there be any doubt that something was going on in the form of corruption. Everything looked clear for a Hillary win until the very end; so the question is: What was done at the end of the night? This is only the small sample of what might have happen in the State of Wisconsin. We also have to consider that the state of Wisconsin had the most corrupt Governor in the state's history.
16
Votes are necessary but not sufficient in our system. Where the votes come from are decisive. It was set up to keep massive states from overwhelming a combination of small states. Otherwise CA, FLA, TX, NY call the shots. In 50 yrs perhaps a different set will call them. You may want what CA and NY want today, but not so much tomorrow.
Change the rules and all campaign strategies change.
(Of course, in any system a candidate has to show up - perhaps in a state like WI)
4
The problem with the Times probability needle in the recent Senate election is that it was all an illusion. All of the votes had already been cast. The probability was based on the votes being counted as they were reported counted over the course of the evening. Yet the outcome had already been determined by the voters even if no one knew what that outcome was until about sevenThis had zero meaning relating to how people voted. It only had to meaning related to the order in which votes were counted. It was little more than a trick to keep readers glued to the Times website the way gamblers are to a roulette wheel. When probability is used in this way it represents a dishonest form of journalism. This kind of approach echoes another transI have seen: headlines and sub headlines that introduce tantalizing topics that are only shallowly written about in the body of an article.
24
I think Rdeannyc doesn't understand what those probabilities meant. The probabilities had meaning in relation to the available information. The criticism is invalid.
Now please explain "transl". Thank you.
26
Since newspapers are not in the metaphysical business, parsing the coverage as being about "an already determined but unknown outcome" versus "an undetermined future outcome" results in a distinction without a difference. The two situations are epistemologically equivalent; there's only a difference for those who still seek to influence the outcome.
If The Times were a crystal ball or a page from Nostradamus, your accusation of dishonesty might stick. As it stands, it's just bunk.
4
"Yet the outcome had already been determined by the voters even if no one knew what that outcome was until about sevenThis had zero meaning relating to how people voted"
This would only be true if there was absolutely nothing shady going on during the vote count. Taking the immense corruption in the State of Wisconsin it is more likely than not that there was something going on during the count to change the outcome.
3
If the weather report says there is 70 percent probability of rain, I pretty much take it with a grain of salt. If they say there is a hurricane coming I know it is as much for ratings as for accuracy. So I panic a bit but still don't pay it much mind. If a friend says there is a 70 percent probability of rain I take it very seriously. Even though what they say comes from listening to the weather report. I trust how they have processed the information more than the original source. Where that leaves me who knows.
5
It leaves you in a very bad place, Mr. Roth, where you believe what you wish to believe rather than evidence from extensively proven (though not infallible) sources that are right before your eyes.
You have inadvertently nailed what's at the heart of many of our society's problems today.
4
Wet (probably).
Leaves you fairly helpless, I imagine.
The gross error I recall was not in the use of numbers (agreed, numbers generate too little or too much feeling, ranging from cold indifference to emerged subjectivity (hence, the lone wolf terrorist--turned into a raison d'etre for bans on immigrant visits or massive overhauls of policies into draconian authority). The error I recall was in logic: the definition of lying, your assertion a lie required the condition of intent.
In doing so, you limited a lie to a special or specific condition--and substituted one type of lie (the intentional lie) for the larger whole. This exclusionary logic broke down the clarity between truth and falsehood, but more importantly served to enable a liar like Trump, who habitually lies and may or may not do so knowingly. Assessed less critically, the damage done was still in full effect!
Example: the "Merry Christmas" lie; whether done with knowing intent or for political advantage, it perpetuates a myth and creates divisiveness, as did Reagan's welfare queen. Your argued definition was so narrow it made the category useless and normalized the impact!
Finally, lies can be overstated or understated--a point not addressed in this year of lies, but important to understanding how rhetoric is shaping and justifying the new social order and political economy. Intent aside, Trump's lies have attacked London's mayor, the FBI, defended white supremacy, derided the media, victimized women, and protected Russia. Outcome is more important than intent.
103
Put another way, the definition of a word does not depend on its instrumentality.
7
Prove where Trump defended white supremacy.
“In doing so, you limited a lie to a special or specific condition--and substituted one type of lie (the intentional lie) for the larger whole.”
There is no such thing as an intentional lie. If you don’t know what you said is false, it’s not a lie. Trump doesn’t lie all that much, because he doesn’t know what he is saying is false. He just doesn’t care.
2
The election probabilities, which were based on the polls, got it badly wrong. Probably among the believers of the polls were the Russians and the Trump campaign. And how would they have reacted? Would they have realized that desperate actions were needed to prevent what the polls had firmly predicted? Desperate actions involving their coordinated efforts?
7
Trump (and his family) so thoroughly believed the polls (as I did!) that he did not even prepare an acceptance speech. And his children had come to him, and told him "don't expect to win, prepare for the very worst outcome (a miserable landslide loss)".
That doesn't sound like a candidate (or family) that had colluded with "Russkies" or had some grand plan for winning by illegal means -- does it?
1
The election probabilities, which were based on the polls, got it badly wrong. But, among the believers of those polls probably (there's that word) were the Russians and the Trump campaign. Each desperate to find some way to change the results. Wouldn't that probably be a strong incentive to collaborate, to work together against the common enemy? When is there evidence of the Trump campaign contacting the Russians? Was it when the polls were so firmly predicting a Clinton victory?
21
Pete, read the Op-Ed again. The polls did not predict a Clinton victory. They gave a probability of one.
3
Trump's favorability rating in late October 2016 was the lowest in modern presidential polling and hostility towards him was not confined solely to Democrats. "Relying largely on opinion polls, election forecasters put Clinton’s chance of winning at anywhere from 70% to as high as 99%, and pegged her as the heavy favorite to win a number of states such as Pennsylvania and Wisconsin that in the end were taken by Trump.....While the exit poll results were consistently accurate throughout nearly all of the Republican primaries, they were wildly and broadly inaccurate in the Democratic primaries, exhibiting a pervasive intra-party shift to the detriment of Sanders (i.e., Hillary Clinton’s vote count percentages consistently exceeded her exit poll percentages, the disparity often far beyond the poll margin of error)."
What explains these polling anomalies that defy the science?
http://www.pewresearch.org/fact-tank/2016/11/09/why-2016-election-polls-...
http://www.mintpressnews.com/donald-trump-warned-of-a-rigged-election-wa...
https://harpers.org/archive/2012/11/how-to-rig-an-election
http://electiondefensealliance.org/ and http://codered2014.com/
Those polls only came about really late in the campaign -- far too late to coordinate a complex strategy involving a foreign power, hackers or infiltrating Facebook.
Also: it's past a year now since Trump won, and SO FAR there is not a shred of credible evidence of any real conspiracy here, or any real foreign intervention (like hacking voting machines) and if there was, I assure you that the desperate, frantic left would have long since impeached Trump in Congress. But in fact, they've done exactly NOTHING....zero, zip, nada.
They have no evidence, just pathetic "conspiracy theories".
1
Instead of probabilities, perhaps one should look at confidence intervals. This is where one gives a range, and one is 90% certain of an event being in that range. So, for example, you might say you are 90% confident that candidate X will receive between 48 and 53% of the vote, instead of saying the candidate will win with 50.5%.
Even with confidence intervals, one will be wrong some of the time -- ideally 10% of the time -- but it is better than attempting to make an absolute prediction.
26
While I like the idea, it doesn't work here. There is not merely a 90% chance that the candidate will either win or lose. That is 100%.
5
Confidence intervals are useful when you are trying to estimate the value of some unknown parameter (like the final vote tally, or some physical parameter like the weight of something). But in a situation where the actual vote tally doesn't determine who wins (as in our electoral college system), confidence intervals don't make sense. They wouldn't even make sense if it was a "whoever has most votes wins" system, since the degree to which the winner outperforms the winning 50%+1 vote is irrelevant.
Instead, you should regard these probabilities as being similar to probabilities of a horse winning at the track. Usually those are quoted in terms of betting odds (2:1 odds would correspond to a 1/3 probability of a win if a racetrack offered fair bets (they don't!) so if you bet consistently at a fair racetrack at 2:1 odds, 1/3 of the time you should win, taking home your original $2 plus winning an additional $4, or twice your bet, and 2/3 of the time you will lose $2, so that on average the $4 winnings 1/3 of the time exactly cancel the $2 losses 2/3 of the time.)
The thing about betting odds (and the probabilities related to them) is that they are for one-off events, exactly like elections (win or lose?), today's weather (rain or shine?) and horse racing (go to the window or throw away the ticket?)
1
CAC, if you read the actual polls, you will see that is exactly what they do say. It is the media that eliminates the interval although they sometimes put if in the form "there is a a 90% probability that candidate X will receive within 2.5% of 50.5%."
Mark, read again what CAC wrote. It is not what you wrote.
I had to take Probability and Statistics in college for my major and I dreaded it. But I had a good professor and he really opened my eyes. I use what I learned from him almost every day. He actually changed the way I think.
I had to make a presentation the other day to the governing council of a church about their investment philosophy and strategies. They were all successful people in their professions and businesses. But I had a hard time getting across the simple concept of expected return and the asymmetrical risk that long dated bonds pose to investors this close to the zero bound, regardless of where rates go in the future.
A big problem I had was that most people want certainty in decision making about future events that are subject to uncertainties. Rigorous analysis can reduce greater uncertainty to smaller uncertainty and quantify the risks and rewards. But not eliminate risk, even though human nature makes us yearn for that.
I once had a boss who said, "Get three bids, take the lowest one. What's so hard about that?" He wasn't a very good businessman.
83
Well, that's the ultimate human conflict -- isn't it? We all want to eliminate ALL RISK, but it is never possible. For example, you can lead a squeaky clean healthy life and never smoke or drink, weigh an ideal weight and exercise daily -- and still get cancer.
That is very hard for people to accept. We want to think we can "bargain with God" (even if we are atheists!) and if we do X then we will receive result Y.
But there are NEVER guarantees like that in life -- or finance. I've seen people who did "all the right things" who were wiped out and destroyed by the 2008-2012 financial/housing crisis. I've also seen people who were out-and-out blithering financial idiots....but who due to plain dumb luck, made out like bandits.
The reality is that LUCK plays a huge, enormous role in OUTCOMES.
1
"The rise of big data means that probabilities are becoming a larger part of life. And our misunderstandings have real costs."
If you want to raise the probability that an article will remain with you, leave the best till last.
Which is what you did here David Leonhardt, by finishing off this piece with one doozy of a last paragraph about President Obama minimizing the importance of Russian hacking because of his "certitude" that Trump could not possibly win.
Talk about the real costs of human misunderstandings, or rather, over-gaming the probabilities.
I don't think Democrats will make that same mistake twice, or at least my mind tells me there's a high probability that they won't.
Or will they?
243
ChristineMcM: But who would have guessed that nearly 3 million voters for Hillary wouldn't count? The idea that Trump won is really not accurate - the Electoral College won, and 3 million voters lost!
5
They will. And the rest of the public are also underestimating the cost of gerrymandering in actually being able to oust unwanted legislators. The effort required in 2018 to achieve that goal will be enormous because most Americans remain too lazy to register to vote and to go to the polls when they are registered. Meanwhile, Republicans are funded by the super rich who have made a decades long investment that is paying off for them short term in real dollars even as it eats away at the American economy long term.
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What disappointed me about the comment was that it opined that a Democrat, Obama or others, would have assigned concern to Russian election meddling only if he or they felt that Trump could win. The focus was on political party concerns and not protection of Constitutional or sovereignty issues. Once in power, he or they are accountable for much more than political jousting.
The big thing that probabilities miss is consequences. That 10% increase in the probability of a serious war with Syria ignores the consequences of a serious war with Syria - the deaths of tens, hundreds, or thousands of people, and the ripple effect of those deaths on both countries. Reducing consequences to phantoms, the un-visualized outcomes of those probability events, weakens the decisions. Leaders make decisions based on probability of success or failure, and have no empathy or ownership of the consequences. Perhaps the way to present probabilities is "This course of action increases the probability of a war with (for instance) North Korea by 15%. If that war happens, you will be the first casualty, by law." Now the leader has some investment in the consequences, which otherwise would all be borne by others... and the weight of their decisions and actions will be more internalized and the decisions will be more 'real' to them. And possibly even better for the rest of us.
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Yes. One has to somehow combine the probability of something bad happening with the penalty function when that occurs. A low-probability event that is very likely to kill me is an event to be avoided. Most people do not do that computation, even implicitly.
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Exactly. A 10% increase in chance of a war that will, on average, kill a million should be presented as a decision that kills 100,000.
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Jim, there is a concept call expected value. It is roughly the probability of an event times its cost. The thing is to compute it, you must first compute the probability.
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There is a second problem -- not just understanding probabilities but understanding uncertainty in probabilities. Weather forecasts and intelligence service reports come up with probabilities that are based on partial information, so the 40% chance of snow or 2% chance of full-scale war might actually be higher or lower if we had more data.
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Any % chance should always be reported with an associated +/- (random) error. That is an important part of the "story" discussed in this column.
But the primary quantitative version of the "story" is the systematic error. Making that type of error work as much in your favor as possible is always the key. But the first step is realizing that it is there.
Dennis, you understand probability and statistics better than Leonhardt. Leonhardt says "when the unlikely happens, people scream: The probabilities were wrong! Usually, they were not wrong. The screamers were wrong." Uh, no, this is true only if we accept that the stated probability is based on full information and an accurate understanding of the forces that determine the outcome. Most election outcome probabilities ("forecasts") are based on rather imperfect statistical correlations and, often, flawed theories and models of voting behavior. So the true probability of an outcome is unknown--it is estimated, and the estimate can be WAY wrong. To deny this is to deny that a stated probability ("forecast") can ever be wrong, which might make the statistician happy but renders his or her work worthless.
Right Dennis. That is called the variance. Leonhardt tried to illustrate that by the width of the various colored regions around the pointer, but that is a very crude method, and it is not clear hoe he computed it.
As a retired electronics engineer, I find numbers easy to use or comprehend. Usually the first question asked is, how did you get these results? That "drilling down" process can be quite illuminating and at times worth more than the numbers alone.
Too, probabilities can be viewed in different ways. As an example, if one played a game similar to roulette and there were only two colors and an equal number of each, the odds of landing on one color would be 1/2. Each roll would be 1/2, but landing on the same color three times in a row would be, 1/2 *1/2*1/2 or 1/8.
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As any gambler knows, the term "odds" is not the same as the term "probability." If an event has a 50% probability of occurring then the odds that it will occur are 1:1.
http://stats.seandolinar.com/statistics-probability-vs-odds/
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@tanstaafi
Thanks. The odds or probability of finding me in a casino are the same, ZERO! Happy Holidays.
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This is a great article. People almost certainly do understand statistics better than the examples suggest, though. Most get the jist of a weather forecast. Around here, when the prediction is for a 2% chance of rain, that means black clouds will be in the vicinity and the rain could reach the ground. The problem with probabilities you see in the media is that most are unique, and nobody knows what the predictive model looks like. Chances are people won’t take the number seriously. They might be willing to reach a conclusion, however, if the odds are strong enough and it corresponds to what they think already. The stock market collapsed overnight when Trump made his Midnight Charge. Then everybody thought things through and the probabilities turned upside down, even though the facts didn’t change at all.
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I disagree. In my experience, people may have figured out what a 40% chance of precipitation is (you did not mean to say 2% chance of rain, eh?), but they have not been able to transfer that learned and implicit knowledge to any other area. People think that if one thing is happening at a 60% rate when last year it was happening at a 64% rate, they automatically "reject the null hypothesis" and just "feel" that the difference is significant.
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What in the world can you mean by "most [probabilities] are unique"? Do you know what "unique" means? Please look it up.
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Yes - 2% is statistically meaningful in Arizona.
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It is one problem for a democratic society that many people do not understand probability, statistical forecasts and scientific reasoning. It is a far more serious problem when many of the elected officials and the officials they appoint do not understand probability, statistical forecasts and scientific reasoning.
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And it is an even far more serious matter when senior officials understand probability very well and deliberately choose to use their knowledge to mislead the public and subvert the law for their own benefit.
Specifically Paul Ryan, Mitch McConnell and Steven Mnuchin mislead on tax reform, Kris Kobach misleads on voter fraud, and Scott Pruitt misleads on environmental protection.
While Donald Trump misleads on all the above and much more, I would not give him credit for understanding probability on the basis of the performance of his casinos.
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Worse yet, some people CHOOSE not to even pay attention to the efforts and fundamental principles underneath the investigations and analysis that are used,
and just cling onto certain behaviors and beliefs based on self interests or instincts. The difference between fast and slow thinking.
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John Roberts comments in the Wisconsin gerrymandering case about "sociological gobbledy-gook" makes one wonder if he understood the arguments being presented.
https://www.washingtonpost.com/news/monkey-cage/wp/2017/10/04/justice-ro...
Attorneys have a notorious aversion to quantitative evidence and mathematical reasoning. Their training is mainly linguistic, not numerical. Because the US has, by far, more attorneys in positions of power like legislatures and regulatory agencies than other countries, our policy-making process prefers that slippery beast, language, over numbers and science.
https://apw.polisci.wisc.edu/APW_Papers/lawyers_in_congress.pdf
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