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Gray and Condorcet

July 8th, 2003 · No Comments

If you’ve ever studied political science, you probably know about Condorcet circles in voting. These come about when public preferences in an election are arranged such that, for any candidate under consideration, a majority prefers some other candidate. Since, under these conditions, any choice is arguably “irrational” (after all, a majority would prefer somebody else), this is also sometimes called Condorcet’s paradox. Ken Arrow made his academic name with a more technical and elaborate version of the paradox, showing, in essence, that any system of voting (or social ordering) you might devise will be “irrational” in one of five pretty basic ways.

One sort of “irrationality” you can get is the “third party spoiler” effect, as when, for instance, the presence of Nader in a race means that Bush gets elected, even though a majority (even filtered through the Electoral College) would’ve preferred Gore. One way we try to deal with that in our two-party systems is through primaries: we winnow down a fields of liberal and conservative candidates through an internal, party-centered process, so that candidates who are relatively close to each other don’t end up stealing votes from one another in the general election.

As Arrow showed, though, you can’t eliminate irrationality in elections; you can only substitute one kind for another, which you hope is less prevalent and pernicious. In California, the result of the primary system was that Bill Simon beat out the more moderate Dick Riordan in the GOP primary by playing to the hard right, and Simon proved unelectable even facing the unpopular Gray Davis. This was especially sad, because among the general population, there almost certainly wasn’t a Condorcet circle here: a majority would prefer Riordan to both Davis and Simon in pairwise contests.

Davis now claims that the current recall effort is just “sour grapes” on the part of those who lost at the polls last time around. But changing the order of voting changes the outcome: in a recall election, voters give Davis an up or down vote first, and then select between other candidates, rather than the other way around. A recall, then, seems like a perfectly reasonable way of compensating for a predictable but lamentable flaw in the usual way of carrying out elections.

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