Let's consider the prospects for burial in three candidate Condorcet when cycles are resolved by random ballot. In particular, let's consider the electorate profile given by
40 A>C>B 30 C>A>B 30 B>C>A There is a potential for burial strategy here: if the 40 A>C>B voters bury the Condorcet candidate C, they create an artificial A beats B beats C beats A cycle, in which "C beats A" is the weakest defeat, so unless C takes counter measures, most deterministic Condorcet methods reward A for going ahead with the burial of C. But when cycles are resolved by random ballot, the respective probabilities for A, B, and C are 40, 30, and 30 percent. If the 40 voter faction has a high regard for C relative to B, which we can denote by 40 A>C>>B, then the burial doesn't pay. Note that the sincere ballots show that A and C are clones, so the most likely case is indeed that A and C are closer to each other than to B. However it is possible that the true feelings of the faction of 40 voters are more like 40 A>>C>B. If so, there are still two sub cases: Subcase I: The 30 B>C>A voters have relative preference strengths of 30 B>C>>A. In this case 70 percent of the voters are of the opinion that C is closer to B than to A. But this contradicts the 30 sincere C>A>B voters. So subcase I is not very reasonable or likely. Subcase II: The 30 B>C>A voters have strengths of 30 B>>C>A. In this subcase we have 40 A>>C>B 30 C>A>B 30 B>>C>A. In this case we see that C is a very low utility Condorcet candidate. Sincere approval votes would make A the winner. So it shouldn't be considered a bad thing that A gets 40 percent of the probability and C only gets 30 percent of the probability in the case of an artificial cycle created by burial of C. ---- Election-Methods mailing list - see http://electorama.com/em for list info
