Condorcet.orgRanked Pairs is a Condorcet Criterion method. This means that it always picks the Condorcet winner when one exists. A large number of other methods have been suggested which do the same thing. I consider Ranked Pairs to be the best of these methods, although some of them are rather similar and therefore the arguments against them can't be as strong. I won't go over every Condorcet completion method that has ever been proposed, but instead suggest some problems they may suffer from.
Throughout this site, I have mentioned various properties of Ranked Pairs that other methods lack. Some other Condorcet methods lack these properties as well.
For example, in my page on positional methods I mention the fact that Borda is strongly affected by how many candidates represent a particular ideology. That is, the more candidates representing a particular perspective, the more likely it is to win. Plurality is well known to have the opposite problem, what people call vote splitting. This is called the problem of "clones": running a number of virtually identical candidates can affect the result. Some Condorcet Criterion methods actually have the same problem to a greater or lesser extent, but Ranked Pairs is designed to avoid these problems.
Consider an election which is decided primarily on some linear issue, but also is decided on a non-linear basis. For example, if the candidates tend to fall into either a left, middle, or right camp (linear), but within each camp, candidates are chosen based on various elements of personality (non-linear). We would like someone in the median camp to win even though the election as a whole is non-linear. This is of course closely related to the problem of clones, since if an ideology lost simply because too many candidates represented it, and there was a conflict of the majority preferences among these candidates, then this would be a clone problem.
Some Condorcet criterion methods allow the defeat of the central candidates in this circumstance.
I was rather critical of the fact that in IRV, it is possible that by doing nothing but decreasing a candidates position on some ballots, you can cause that candidate to win. Some Condorcet completion methods have the same problem, but not Ranked Pairs.
I also pointed out that in IRV a candidate can win the election, even though that candidate would also "win" if voters were asked to select the worst candidate. All with voters giving their sincere honest preferences. Once again, some Condorcet criterion methods also have this strange behaviour, but not Ranked Pairs.
To really understand Ranked Pairs, you have to think about how you could interpret various kinds of evidence. All methods use certain kinds of information, and ignore other kinds. For example plurality only uses first preferences. This does not make much sense to me, but if you assume that this is correct, then plurality becomes the only reasonable method.
So, let us consider what kinds of information Ranked Pairs uses, what kinds it does not, and why. Clearly it uses the voters' direct comparison between two candidates. When deciding whether A or B wins, a major part of the decision is the number of voters who prefer A to B, and the number who prefer B to A. As is mentioned in my page on Arrow's Theorem, it is not possible to rely on this kind of information alone. Ranked Pairs is a usable method because it also allows paths of these pairwise comparisons to be used.
In other words, if we have evidence that A is better than B, B is better than C, and C is better than D, then we have evidence that A is better than D. This is the kind of path of majority decisions that Ranked Pairs locks as part of the procedure.
However, Ranked Pairs ignores certain information about the comparisons between candidates. For example, if B has a greater loss to C than does A, that is a plausible argument for A against B. To understand why Ranked Pairs does not use this information, it helps to see an example.
60 C B A
40 A C B
The reason you might think B's greater loss is evidence between B and A would be that you thought that it showed that B was much worse than C, while A was only a little worse. Examples like the above suggest that the choice is only more obvious between B and C, not necessarily that there is a bigger difference. For example, this might be the result if a parliament is considering 3 versions of a bill. B is the original. A makes a substantive change. C just removes a spelling error.
As a result of arguments like this, Ranked Pairs restricts itself to using direct comparisons, and paths made up of direct comparisons. If we restrict ourselves to these paths, then we might ask, if I have a majority saying A>B, then what might prevent me from putting this in the final ranking? Consider the case where the only paths that contradict this victory have lower margins. Then the question becomes, should I ever allow evidence made up of a large number of lower margin victories to over-rule a higher margin victory?
To answer this question, I'll suggest a simpler, less realistic, problem. Let's say that you have a test that you can perform on candidates to find which is superior. The test gives you its guess, and a percentage for certainty (much like fingerprinting). You do two tests.
A>B 70%
A>B 60%
So, what's your true certainty? If you assume the tests are independent, the answer is clear. 1-(1-.7)*(1-.6). But what if you do not know they are independent. Then it gets harder. All you can say for certain is that your certainty is at least 70%.
Independence is the starting assumption for Borda. Unfortunately, voter decisions are likely to be highly dependent, and any assumption of independence tends to be exploitable strategically. Therefore, Ranked Pairs avoids assuming any level of independence. However, if you are unwilling to assume any independence, multiple lower margin victories will never be able to over-rule a higher level victory. This suggests that you should lock victories starting from the highest margin, just as Ranked Pairs does.
So, Ranked Pairs isn't just a plausible sounding procedure, or a procedure that manages to meet certain desirable criteria. It is the procedure you must follow if you make certain plausible assumptions about how evidence from ballots should be interpreted.