Warren Smith writes: > I will sketch a proof that, in Schulze beatpaths voting in "random" > N-candidate V-voter elections (V-->infinity, N fixed): > with probability > a positive constant C (where C goes to 1 as > N-->infinity): > at least a constant fraction K of the voters (where K goes to 3/4 > as N-->infinity) > will regard it as strategically forced that they order D>E for at > least one > candidate-pair {D,E} for which they honestly prefer E>D. By > forced I mean, > they'll feel if they don't do this, they'll have lower expected utility.
Can you follow up with a proof sketch of the fraction of debaters who have no ethical compunctions about inventing a scenario and then arguing that they can prove how a supermajority of a population will *feel* about that invented scenario? Beyond the obvious inefficiency, one reason that current electoral systems are loath to repeat elections (even in substantially similar form, such as runoffs) is that repetition permits a variety of strategic considerations between iterations, including focused violence or intimidation. Outlining the extent to which this is true in "random" elections with arbitrarily large numbers of both candidates and voters is not particularly informative. As the number of candidates increases without bound, the "distance" from any given point to the candidates, or between candidates, tends to decrease -- much in the same way that distance between points converges to unity in high-dimensional space. Given that Condorcet methods are susceptible to order reversal, that is exactly the kind of scenario where you would expect it to be more likely to have an effect, but the per-voter benefit averaged over "random" elections goes down as the number of candidates goes up. So accepting, arguendo, that 75% of voters might -- a posteriori -- gain expected utility from strategic order reversal, to conclude how they would feel about that requires an argument that they care more about the vanishingly small gain in utility than they do about honesty in voting. Michael Poole ---- Election-Methods mailing list - see http://electorama.com/em for list info