Proofiness - Charles Seife [67]
However, when the city of Minneapolis proposed using instant runoff voting for some elections, opponents promptly sued, claiming that the scheme is unfair—more specifically, it’s unconstitutional because it doesn’t count every vote in precisely the same way, an argument that the Minnesota Supreme Court promptly knocked down. However, it’s absolutely true that instant runoff voting has disadvantages over plurality voting. Ballots in plurality elections are very simple—you simply vote for one person—yet as the Minnesota election showed, people screw them up all the time. Imagine all the ways that people would fill out a “rank three candidates in order of preference” ballot incorrectly. The error rate of the election would go through the roof.
Another drawback of instant runoff voting is that it doesn’t always give the answer that the voting public thinks is best. Indeed, in the above example, Dean Barkley could argue that in fact he should be elected, because that choice would make the most people the least unhappy. To see this, take the instant runoff results above and modify them slightly. Every time a voter ranks a candidate in first place, give that candidate two points to represent the voter’s strong desire to get that candidate elected. Every time a voter ranks a candidate second, the candidate gets one point, signifying that the candidate isn’t the voter’s ideal choice, but is not too horrible. Finally, every time a voter ranks a candidate in third place on a ballot, the candidate gets zero points for being the greatest of all evils. (This scheme is known as a Borda count, and, like instant runoff voting, it is often floated as an alternative to plurality votes.) Total up the points. All of a sudden, the election looks very different:
2,722,653 points for Norm Coleman
2,585,760 points for Al Franken
3,278,940 points for Dean Barkley
Dean Barkley wins handily—by virtue of being the least loathed candidate overall. Franken voters prefer Barkley to Coleman, and Coleman voters prefer Barkley to Franken. Barkley is the compromise candidate that everybody can live with.
In the Minnesota Senate election, three different voting schemes—plurality, instant runoff, and Borda—would have yielded three different victors, even though the voters’ preferences were identical in all three hypothetical scenarios. You can take exactly the same ballots and look at them in three different ways and come up with a perfectly valid argument about why each candidate should be elected to the Senate.
This illustrates a central problem with voting. Reasonable people can look at the same pile of ballots and come to very different conclusions about who should win an election. While plurality voting, Borda voting, and instant runoff voting each have their advantages and disadvantages,67 none can claim to be the fairest way of electing a politician; they’re all flawed. It’s a mathematical truism known as Arrow’s theorem.
In the 1950s, economist Kenneth Arrow proved that it’s impossible to have a perfectly fair election system. But what does “fair” mean in this context? Well, there are certain characteristics that you would expect a fair election to have. One seems ridiculously obvious: there can’t be a dictator who determines the outcome of an election; there can’t be an individual whose vote overrules everybody else’s. A fair election implicitly follows this “no dictators” rule. Another obvious condition: a vote shouldn’t flout the unanimous will of the people. If everybody in the nation votes for Ross Perot, then, by God, Ross Perot had better win the election. A fair election also implicitly follows this “unanimous vote” rule. Finally, there’s a third characteristic that’s a little less obvious: the ranks of candidates in a perfectly fair election should