Paul K. is going to think that I have too much time on my hands, since this posting is strictly for theoretical purposes, namely to try to imagine how close we might get to the "Small Voting Machine," the SMV that was posited by Alex Small two or three years ago. Here's a stab at the idea. Imagine that you had unlimited computing power with an infinitely fast computer to process the rankings submitted by the voters. This method is a ballot by ballot Declared Strategy Voting method like Rob LeGrand's in which ballots are drawn in random order from the stack of ballots, and by some rule an approval cutoff is applied to each ballot in succession. The winner is the candidate with the greatest approval total. In rob's method, approval strategy A is applied. The approval cutoff is placed next to the name of the candidate with the current highest approval on the side of the name of the candidate with the next highest approval. In the method I propose every possible cutoff is tried, and the one that gives the best result is used. Here's what I mean by trying a cutoff: tentatively place the cutoff at some level of the ranked ballot, and then run the rest of the ballot by ballot DSV one hundred times to find the distribution of winners that results from using that cutoff. After you have done that with all of the possible cutoffs on the ranked ballot, go with the cutoff that produced the most favorable distribution of winning candidates. (most favorable relative to the ranked ballot in question, of course) Then go on to the next ballot, and repeat the whole procedure. Of course this method lacks practicality. But perhaps there is some way to approximate it in the same way that automatic chess machines approximate the corresponding chess strategy. What do you think? Forest
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