Opinion

Why Ranked Pairs

This page expresses the case for using Ranked Pairs to determine the winners of preferential ballot elections. Whereas the rest of this web site is facts and tools, this section is opinion. You should form your own opinion.

Condorcet's Principle

If a candidate beats every other candidate head-to-head, that candidate should win.

Such a candidate is called a Condorcet winner, in honor of the Marquis de Condorcet (1743–1794), the French mathematician and philosopher who was a pioneer for equal rights, the abolition of slavery, and the rights of women. If the voters are asked whether they prefer Candidate A or Candidate B, A or C, A or D, A or E, and the answer comes back Candidate A every time, then Condorcet would say, “Give the voters what they want: Candidate A wins!” A preferential ballot vote counting method that always selects the Condorcet candidate, when one exists, is called a Condorcet method.

If one models the political spectrum one dimensionally (a big assumption), there is always a Condorcet winner, namely the candidate closest to the median voter. In this sense, it is fair to say that Condorcet methods reward centrist candidates.

How often is there a Condorcet winner? For real world elections in the United States, almost all of the time. So if you believe in Condorcet's Principle, you understand what democracy means to you in the vast majority of cases. Note that this rules out many methods, including Instant Runoff Voting and the Borda Count.

Of course the United States political system is dominated by two parties, so a more interesting question is to understand elections with many candidates. In our real elections there was a Condorcet winner 92% of the time with 6 choices (33 of 36), 87% of the time with 10 choices (398 of 455), and 81% of the time with 15 choices (387 of 475). See Real Elections.

Clone Invariance

Similar candidates should not penalize (or reward) each other, for example by splitting the vote.

With a clone invariant method, two candidates with similar positions can both run without handing the election to a candidate they both oppose. This makes political parties less necessary.

Monotonicity

Ranking a candidate higher should never hurt that candidate.

With a monotone method, a voter never has a reason to rank a favorite candidate lower in order to help that candidate win. This allows voters to vote more honestly.

Last Place Loser Independence

If the last place loser drops out of the election, the outcome should not change.

The “last place loser” is the winner of the “who is my least favorite” election where everyone's preferences are reversed. With a last place loser independent method, there is always at least one candidate (usually more) whose participation does not affect the outcome of the election. This decreases the influence of fringe candidates.

The game theory of preferential ballot elections

Preferential ballot elections allow voters to specify a 1st choice, a 2nd choice, a 3rd choice, and so on. Since they collect more information from voters, preferential ballot elections often produce winners who better represent voters than single vote ballot elections, in ways that can be made mathematically precise.

However, since more information is collected from voters, the question of how to determine the winner of a preferential ballot election is more complex, both mathematically and philosophically. One of the subtleties is that there are many ways to determine the winner of a preferential ballot election, and often these different methods lead to different results. More importantly, each vote counting method has its own game theory, which incentivizes candidates and voters to behave in certain ways.

For example, single vote ballot elections incentivize candidates to join one of two major political parties to avoid “splitting the vote” with other candidates who have similar political positions. Furthermore, voters are incentivized to vote for one of the two major political parties to avoid “throwing their vote away.” This mathematically precise effect, known as Duverger's law, is very evident in American politics, which has favored two major political parties for most of its history. If you want to change how the players play the game, then change the rules of the game.

The four properties above incentivize voters to vote more honestly and candidates to seek more centrist positions. They also decrease the influence of political parties and fringe candidates. The only major preferential ballot vote counting method with all four of these properties is Ranked Pairs, defined in 1987 by the economist Nicolaus Tideman, and it is the method this web site uses to determine the winner (and the ranking of all of the candidates). Philosophically, Ranked Pairs chooses the ordering of the candidates which gives the highest priority to the greatest margins of victory in all of the head-to-head contests (where only two candidates compete at a time). Professor Bray argues that Ranked Pairs is the best preferential ballot vote counting method to use if you want to reward centrist candidates (via Condorcet), independents (via clone invariance), and honest voters (via monotonicity) while minimizing the influence of fringe candidates (via last place loser independence).

Professor Bray explores these questions in his “What is Democracy?” video series.

Other methods

Instant Runoff Voting* is neither Condorcet (and hence not good at picking centrist candidates) nor monotone (so that, for example, voting for a candidate can actually decrease their odds of winning, in some circumstances). The Borda Count is monotone, but is still not Condorcet, and incentivizes voters to vote very dishonestly in some cases, including highly ranking candidates that they don't like, as a way of hurting candidates they view as competition for the candidate that they do like. Neither of these methods should be used to select a single winner,** if the above considerations are a concern. On the other hand, the Schulze method, which is Condorcet, clone invariant, and monotone, is a reasonable method, even though it is not last place loser independent. However, while it always determines a winner, it does not always provide a ranking for all of the candidates, even when all ties are broken, which could be a problem for some applications.