The comments thread on the Crooked Timber edition of my last post led me to this site (hat-tip: novalis), advocating Condorcet voting and presenting a critique of the instant runoff/single transferable vote , the core of which is

IRV has serious problems. It allows a sufficiently small minority of voters to safely register “protest” votes for minor-party candidates–but only as long as their candidate is sure to lose. As soon as their candidate threatens to actually win, they risk hurting their own cause by ranking their favorite first, just as they do under our current plurality system. IRV is therefore unlikely to be any more successful than plurality at solving the classic “lesser of two evils” problem.

It’s straightforward to show, however, that this problem can only arise if your preferred candidate would be the loser in a Condorcet system. Hence, voting strategically yields the preferred Condorcet outcome.

To see how the argument works consider three candidates A,B,C and suppose that A’s supporters rank ABC, C’s supporters rank CBA, and that no candidate has an absolute majority. Then (regardless of the preferences of B’s supporters), B is the Condorcet winner. If B has the most or second-best supporters, then a (weakly) dominant strategy is for everyone to vote in line with their preferences, leading to B’s election. Suppose however that B has the smallest number of first-preference supporters and that A would win over C in a pairwise contest. Then, as stated in the critique above, the optimal choice for C’s supporters is to vote strategically for B, so that B finishes the first round ahead of C. The distribution of preferences then ensures that B is the winner. So, in this case, strategic voting does not produce the “lesser evil” as far as the majority of the electorate is concerned.

Things can tricker when there are n (greater than 3) candidates with a serious chance of winning. But the problems for Condorcet are even worse, since the method requires n(n-1) pairwise comparisons.

Taking this a bit further it seems likely that, whatever rule is chosen for resolving cycles, an implementable Condorcet system would be vulnerable to exploitation by strategic choices to run (or not run) particular candidates whose function would be to tip the balance in favor of some other candidate.