Americans might be surprised to learn that majority rule is a terrible way to decide most elections. Among other things, shrewd voters can manipulate majority rule by voting against their true preferences. Fortunately, computer scientists have figured out there are better ways—the approaches called the Nanson and Baldwin methods.
There’s a universe of voting systems out there. Popular among social scientists is the Borda count, in which voters rank candidates, the ranks are converted to points, and whoever tallies the least points wins. (Nanson and Baldwin are variations on Borda, in which the Borda tallies are used to eliminate low-ranking candidates before a final tally is computed.) No one system is perfect, though, and nearly every one is susceptible to what’s known as manipulation or, more politely, strategic voting. (The exceptions to this rule include dictatorship and not allowing pre-selected candidates to win, even if voters would want them to.) That’s what you call it when someone votes for a second-choice candidate that stands a better chance of winning than her first choice, and you don’t need to look far afield for examples. It was a hot topic in the 2000 United States presidential election, when some viewed Ralph Nader as a spoiler candidate and urged liberals to vote for Al Gore instead.
Strategic voting isn’t obviously a bad thing, but a system like majority rule that’s susceptible to manipulation also encourages people to suppress their true political preferences.
Strategic voting isn’t obviously a bad thing, but a system like majority rule that’s susceptible to manipulation also encourages people to suppress their true political preferences. As a result, political philosophers say, elections and subsequent debates do little to generate fresh ideas. But if there’s no manipulation-proof system, what can we do?
As the saying goes, the perfect is the enemy of the good, so University of Toronto computer scientist Jessica Davies and her colleagues set out to discover what’s good—at least, whether the additional steps in the Nanson and Baldwin methods help make them harder to game than Borda.
The team proved that manipulating those three is so complex that in the toughest cases even verifying the efficiency of a proposed strategy would take an impractically long amount of time. But the real world is rarely that tough, so they also tested several more practical algorithms for influencing elections. For instance, a voter who knows others’ preferences ranks her favorite candidate first and ranks all others opposite to the rest of the electorate—if enough people do that, it could cancel out the others’ choices. Although Borda was theoretically as hard to manipulate, it was in practice very easy to influence. In a series of computer simulations, the team’s algorithms could manipulate Borda voting more than 99 percent of the time, compared with about 75 percent for Nanson and Baldwin voting.
Davies cautions that the results really only apply in a world in which potential manipulators know how everyone else has voted. Still, "I do think that they would be less likely to try to manipulate a Borda election," she says in an email, "and after that, even less likely to try to manipulate elections where there are elimination rounds."