When a University of Illinois at Urbana-Champaign psychologist and his graduate student combed through eight years of APA presidential votes, they made an interesting discovery: Different voting methods don’t yield different results. This finding is contrary to long-held claims by voting theorists that election results can shift depending on the voting rules used.

“Our empirical results appear to suggest that voting methods are much ‘better behaved’ in real life than they are on paper,” says Michel Regenwetter, PhD.

He and graduate student Anna Popova analyzed data from eight APA presidential elections, which included as many as 20,000 ballots each and asked voters to rank five candidates, rather than select only their top choice. The researchers then ran simulations on the ballots to see how the results would change if APA used six other voting methods, including simple plurality voting, which is the type the United States uses for its elections, and rank-ordered Borda count in which voters rank candidates, each ranking gets a score (say “2,” “1” and “0,” if there are three candidates) and the candidate with the highest overall score wins. Out of the seven methods tested — which included APA’s actual, instant-runoff method — only plurality voting produced a different winner in only one of the eight elections.

In addition, Regenwetter and Popova found no evidence for the Condorcet paradox, a problem that voting theory predicts should be ubiquitous with majority-rule methods. In it, there’s no clear majority. For example, if there are three candidates and one-third of voters prefer candidate A to candidate B to candidate C, a third prefer B to C to A, and another third prefer C to A to B, each candidate receives an equal, two-thirds majority and the winner is impossible to determine by “majority rules.”

Donald G. Saari, PhD, director of the Institute for Mathematical Behavioral Sciences at the University of California, Irvine, isn’t surprised by these results, but he’s not convinced that they prove that voting methods are well-behaved.

“Based on my own research on voting patterns, these results simply mean that there was very little disagreement among the voters in this election,” says Saari. “And that’s what one expects in a professional society.”

With more contentious elections, he argues, the results would change depending on the voting system used.

Time and more research will tell, says Regenwetter. “I would venture the guess that we will continue to find much more agreement among competing voting methods than theory predicts,” he says.

—B. Azar