Ken Johnson wrote: > > Bart, > > Here's a link to #597, > http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012689.html > (Search the text for "num_candidate=10".)
Thanks. In your 10 candidate, 1 issue trial, are you able to account for why sincere CR, exaggerated CR, Condorcet, Borda, IRV, and Plurality all yield exactly the same average across 100,000 elections? It looks like top-two Runoff is within 0.1% of the same score. Stranger still, exaggerated CR should be equivalent to Approval, but the scores here are wildly dissimilar. I'm afraid I don't trust the simulation. There are too many cases where widely different methods return exactly the same results. I would expect this with two candidates (if the optimal strategies are done correctly), but not with three or more. Also, I think the Approval strategy used is not what is generally recognized as optimal zero-info strategy. You have voters approving all candidates where CR is >= 0. The usual "sincere strategy" is to approve all candidates where CR is greater than the mean CR of all candidates. In the two candidate cases, this should give Approval the same score as the other methods, as one would expect. > The main problem I saw with Approval occurred when there are many > candidates, and when everyone votes based on a single election issue. Do > you know if Merrill simulated this case? I'm sure he did, but the the cases illustrated in his book use two issues (two dimensions) with 0.5 correlation between them-- you could almost say 1-1/2 issues. The graphs go up to seven candidates, but the trends are clear enough that you could extrapolate out to 10. In Merrill's simulations, Condorcet, Borda and Approval all held up well as the number of candidates increased. Utility of the runoff methods and of Plurality dropped steeply as the number of candidates increased. Bart Ingles ---- Election-methods mailing list - see http://electorama.com/em for list info