The Case For Borda Count Voting

Alex Tabarrok makes the case that "The Borda Count is the Best Method of Voting" at the Marginal Revolution blog.

The Borda Count has voter rank the n candidates from most to least preferred and assigns (n-1) points to the candidates. For example if there are 3 candidates a voter’s top-ranked candidate gets 2 points, the second ranked candidate gets 1 point and the last ranked candidate 0 points. The candidate with the most points overall wins.

This approach seems crude, but the proof is in the pudding. He notes that:

It’s well known that the voting methods we use are highly defective, as they fail to meet fundamental criteria like positive responsiveness, the Pareto principle, and stability. Positive responsiveness (monotonicity) means that if a candidate improves on some voters’ ballots, this should not reduce the candidate’s chances of winning. Yet, many voting methods, including runoffs and ranked-choice voting, fail positive responsiveness. In other words, candidates who became more preferred by voters can end up losing when they would have won when they were less preferred! It’s even more shocking that some voting systems can fail the Pareto principle, which simply says that if every voter prefers x to y then the voting system should not rank y above x. Everyone knows that in a democracy a candidate may be elected that the minority ranks below another possible candidate but how many know that there are democratic voting procedures where a candidate may be elected that the majority ranks below another possible candidate or even that democratic voting procedures may elect a candidate that everyone ranks below another possible candidate! That is the failure of the Pareto principle and the chaos results of McKelvey–Schofield show that this kind of outcome should be expected.

Almost all researchers in social choice understand the defects of common voting systems and indeed tend to agree that the most common system, first past the post voting, is probably the most defective! But, as no system is perfect, there has been less consensus on which methods are best. Ranked choice voting, approval voting and the Borda Count all have their proponents. In recent years, however, there has been a swing towards the Borda Count.

Don Saari, for example, whose work on voting has been a revelation, has made strong arguments in favor of the Borda Count. . . .

The Borda Count satisfies positive responsiveness, the Pareto principle and stability. In addition, Saari points out that the Borda Count is the only positional voting system to always rank a Condorcet winner (a candidate who beats every other candidate in pairwise voting) above a Condorcet loser (a candidate who loses to every other candidate in pairwise voting.) In addition, all voting systems are gameable, but Saari shows that the Borda Count is by some reasonable measures the least or among the least gameable systems.

The Borda Count also has the arguable virtue of resolving elections in a single vote and in being relatively simple to implement.

A say "arguable" because the problem with any system that considers second or greater choices in a single round is that it places a greater burden on voters to be familiar enough with all of the candidates to rank them, as opposed to permitting them to only know which one is their favorite. Multi-round voting systems allow voters whose first choice is eliminated in the first round to gather more information about the remaining contenders allowing voters to make a more informed choice about second and subsequent choices. More generally, demanding more research from voters reduces voter turnout.

Comments to the post also note that the name is just horrible from a marketing perspective, and that it greatly inflates the votes of voters who rank more candidates in total. Unlike majority rule, adding irrelevant alternatives can change society's choice. Apart from being a problem in its own right, this opens the door to gaming the set of policies on the ballot. Although the Borda count captures some sort of preference intensity, it still does so in a very crude way. Multiple commentators disagree that it isn't easy to game.

Another comment argues that:

Voting should be an error minimization. We want to minimize the total difference between people's preferences and what happens.

Approval voting will do this. The candidate that will minimize the sum error (that is the number of people that approved of him - those that didn't approve) will be the the candidate that has the most approval votes. Approval voting can also be used for parliaments where people vote for parties.

Also, Borda count focuses on the winner of an individual race, but may or may not bring a proper balance of political parties in a multi-body legislature. Another comment notes that: "until we get rid of the electoral college and the ability of state governments to gerrymander congressional districts, any voting system will just be nibbling at the corners."