Wednesday, January 04, 2012

Pluralities and Choosing Candidates

Romney "wins" the Iowa Caucuses, but only by a hair. More than 3/4 of those voting opted for somebody else.  With so many candidates, this is a case where it might be nice to see what the voters' second and third choices were.  As the field narrows, those preferences will matter, as will whether the voters continue to participate if their first choice is eliminated.

This is also a reminder that when there are multiple candidates and none is a clear-cut winner, there may be no right way to determine the winner.  There can be "cycles" in the voting preference, as illustrated by the Condorcet Paradox.  Weighted voting, known as a Borda Count, is thought of as a way to determine a choice in this instance, though in the textbook example given in the previous link, weighted voting would produce a tie between all three candidates.  More generally, with weighted voting it is possible to change the winner by altering the weights.  That is not a very satisfying result.  Alas, Arrow's Impossibility Theorem says we can't do better than that.

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