Anyone here familiar with the "Ranked Pairs" voting method?

I am trying to understand how it works as it seems to be one of fairest if not the fairest voting methods around. However when reading the Wikipedia page I have gotten stuck when trying to understand one of the examples in the

Also while I am here does anyone think that a different voting method might be fairer still?
I feel that cardinal/rating-based methods are better. Methods like Score voting, Approval Voting, and STAR voting*. Compared to Condorcet methods, they pass favorite betrayal, consistency, and participation, and are immune to the DH3 scenario.
They fail the Condorcet Criterion, but supporters argue that this is a good thing; the Condorcet winner is a good choice when you only have rankings, but with more information (strength of preference) you can find someone even better.
They tend to perform well even with strategy, at least if it isn't too one-sided (STAR is less vulnerable to one-sided strategy, but even Score/Approval's worst case might not be as bad as other methods)
Not to mention their simplicity.
*STAR doesn't pass favorite betrayal (and maybe not the others? Except DH3; it's immune) (plus it kinda-sorta fails monotonicity), and might be worse in the best-case compared to Score, but the hope is that it's better in the worst-case (one-sided strategy), and that failures are rare, while also making things Score/Approval does fail rarer, e.g. later-no-harm.
I'm not sure what you mean by "fair", but here's an argument that utilitarian election methods are fairest for the group as a whole:
And here is a list of voting methods with measurements of Voter Satisfaction Efficiency, a utilitarian measure:
How do you mean "fair"? Fair to whom?
If all you care about is the will of the majority, then RP and/or Schulze are pretty good. STAR is up there as well.
If you care about the entire electorate, and don't want
Condorcet methods including Ranked Pairs hold up terribly against strategic voting. In a high stakes election with good polling I suspect Ranked Pairs would be very unfair. Also beyond that even if you exclude strategy I have questions about the Condorcet winner being the ideal winner. The system is biased towards selecting non-offensive candidates which when applied over an entire government makes idealogical choices about how government should function at a very deep level.
I recommend VoteFair ranking. It’s explained in the book/ebook Ending The Hidden Unfairness In U.S. Elections, which I wrote.
The Wikipedia page named Kemeny-Young method explains the single-seat-winner portion of VoteFair ranking.
If anyone has questions, feel free to start a post about VoteFair ranking, and I’ll answer questions there. (This post should stay focused on the Ranked Pairs method.)
Doesn't make sense to me either. Based on their example, it sounds like it should be more like
Vxy = Vwz and Vzy > Vyz
Because y is weaker vs z, so x>y is considered "stronger" than w>z?
In the example, it happens to be than x and w are both Nashville.
Vnk = Vnc and Vck > Vkc
Because k is weaker than c, n>k is considered stronger than n>c and Vnk is put before Vnc.
The easiest way to think of ranked pairs is it takes the pairwise results and makes a consistent directed graph by reversing only a few of the pairwise results and biasing towards respecting the voter's strongest pairwise preferences.
This rule really assumes that you don't have 100% of the voters giving a preference for every pair and there are no exact ties between candidates. In a situation where you have all pairs but no ties the rule would just be (Vxy > Vzw). In a situation where you could have an exact tie Ranked Pairs is ambiguous about which goes first but something like (Vxy >= Vzw) with the understanding that in theory it is possible, though very unlikely, this random choice could determine the final winner. In practice most voting methods don't handle the case of perfect ties well and in this particular case wikipedia is constructing a perfect tie.
As an aside the authority on this method (essentially the inventor) is active on reddit. We can try and flag
This is Nicolaus Tideman. The way to deal with ties in ranked pairs is discussed in "Complete Independence of Clones in the Ranked Pairs Rule" (Social Choice and Welfare April 1989, Volume 6, Issue 2, pp 167–173). Briefly, the election is a tie among all the results you can get by different ways of breaking the ties in rankings. The simplest way to get a coherent result when there are multiple ties is to begin by establishing a "tie breaking ranking of the candidates" (TBRC) and use is to establish a "tie breaking ranking of the pairs" (TBRP). Pair A is ahead of pair B if the earlier pair in A (according to the TBRC) is ahead of the earlier pair in B, or if, having the same earlier pair, the later pair in A is ahead of the later pair in B. The TBRP resolves all ties as they arise, so you have a single winner. You need to use a TBRC and a TBRP to ensure that ranked pairs will be independent of clones.
Thanks for taking the time respond I think I see what you are saying. Also thanks for pinging the creator! Did not expect to get help from that high up :D
This is why I prefer
Add/Average the scores on all the ballots, the candidate with the highest score wins. No "If/then" clauses, no consideration of the relative preferences of candidates that don't win, just who has the highest total.
This is also an interesting solution. Do you know if it has been tested on any significant scale?
The thing I worry about here is that it might return to an effective FPTP system if most people vote tactically. Because you would maximise your choices chances if you give it maximum score and score every other option at 0.
I made an explorable explanation about ranked pairs and a few other methods (work in progress). It's based off of Nicky Case's explorable explanation.
If you just keep track of who could win, then it's pretty simple. You keep track of who is "alive" and who is "dead" and run through each pair in order starting from the biggest win. Start with everyone "unborn". For each pair, the winner is born and kills the loser. Keep going until the last man is standing. Also, someone who is already dead cannot kill the living (no zombies), but they can kill the unborn (supernatural elimination).
That explanation sounds equal parts silly and tempting! I shall definitely have a look!
Thank you.
Ranked pairs was actually invented by Nicolaus Tideman a Professor in Virginia, I've spoken to him from time to time and if I remember correctly he even did an AMA here.
He actually already replied in this thread! Very cool indeed!