The model of electoral behavior that Anthony Downs popularized in An Economic Theory of Democracy produces a paradox. The chances that I will cast the deciding vote in any election involving more than a few voters are so small that it is irrational for me to devote any effort whatsoever to voting; I might just as well stay home and let others do the work, secure in the knowledge that the election will come out exactly as it would if I had voted. The paradox is that people do vote, opening a huge gap between what a “rational” person (at least according to a narrow definition of rationality) should do and what hundreds of millions of people sctually do.
One possible reconciliation is the “minimax-regret” principle that Ferejohn and Fiorina ( here, gated) dredged up long ago to try to rescue the rational model. The idea is basically that people are motivated above all else to avoid making a big mistake. Imagine, Ferejohn and Fiorina say, that “your” candidate has just lost by a single vote and you didn’t vote. You’d feel just terrible. To avoid any possibility of feeling terrible, then, you’re likely to vote, even though you understand that the event that would make you feel terrible is extremely unlikely.
And here’s where some recent news out of Arizona comes into play. Every now and then it happens that the Ferejohn-Fiorina scenario, which sounds pretty far-fetched, actually does happen, as it did recently in Cave Creek, Aruizona, when an election for city council produced 660 votes for the incumbent and 660 for the challenger. A bunch of Cave Creekers who didn’t make it to the polls presumably spent the next day beating up on themselves for not voting.
All was not lost for some of these benighted souls, however, for the tie vote still had to be decided one way or the other.If Cave Creek were in Minnesota rather than Arizona, they probably would have decided it by staging an endless procession of recounts until they got down to some arbitrary totals that the last court hearing the final appeal would sign off on in a fit of exhaustion. Well, Cave Creek isn’t in Minnesota, and out on the rugged frontier they have a simpler way of settling such disputes. No, it’s not six guns at 30 paces. It’s … cutting cards. Here’s the story, as reported in the New York Times.
All of which leads me to suggest a revision of the probability term at the heart of rational models of voter turnout. It shouldn’t be “the (very low) probability that I could cast the deciding vote for my preferred candidate.” Rather, it should be “the (very low) probability that I could cast the deciding vote for my preferred candidate plus the (.5) probability that my preferred candidate would win the card-cut given that I have cast the tying vote.” A small step for models of voter turnout, to be sure, but one I consider worth a lead article in the APSR (or on second thought, in the AJPS). This is major.