Given the following preference strengths for the A and B supporters, 40 A>>C>B 30 B>C>>A, which of the following preference schedules is more credible or likely for the C supporters? (1) 30 C>A>B ? or (2) 30 C>B>A ? You might think that there is no way of knowing that one is more likely than the other. But try mapping them out in an issue space. It is very easy to make preference order (2) graphically consistent with the A and B supporter preference strengths, but impossible to do the same for preference order (1), unless we allow extremely non-symmetric metrics, where the distance from x to y is very different from the distance from y to x.
I believe that Jameson Quinn is right when he says that most Condorcet cycles are probably artificial, i.e. they are caused by strategic truncation or strategic burial. Condorcet efficient methods that discourage these two strategies will almost always find a Condorcet Winner. The only exception should be in the case of a “low utility CW,” and since ordinal ballots cannot discern between high and low utility CW’s, there either has to be an approval cutoff for the purpose of detecting low utility alternatives or else there has to be a strategic option for defeating low utility CW’s. Consider the following electorate profile, for example: 40 A>>C>B 30 B>>C>A 30 C Alternative C is a low utility CW. Any Condorcet efficient method gives C the victory. But alternative A is the obvious approval winner, so A should have at least some probability of winning. The natural way to accomplish this is for the A supporters to bury C. Deterministic Condorcet efficient methods may or may not give the victory to A as a result of such a burial. But a method that uses a certain amount of randomness to resolve cycles would give alternative A some share of the probability, because such a method would not discourage the burial of a low utility alternative. In particular, when the method reduces to random ballot applied to the Smith set in the case of three alternatives, in that case it punishes the burial of a high utility CW but does not punish the burial of a low utility CW. Any Condorcet efficient method that doesn’t use at least a modicum of randomness to resolve cycles should allow for approval cutoffs and incorporate the approval information in a way that does not punish the burial of low utility CW’s. ---- Election-Methods mailing list - see http://electorama.com/em for list info
