I thought this example might be of some interest. I'm not certain of its import. I'll give the example first and append my comments.
Range Voting with range 0-10; seven alternatives A, B, C, D, E, F, G; 100 voters. Sincere (whatever that means) ratings are given in the table below, whose last line gives the total point score for the alternatives. # A B C D E F G 24 10 9 3 2 1 0 0 22 9 10 0 1 2 3 0 14 2 1 10 0 0 0 3 14 1 2 0 10 0 0 3 13 1 2 0 0 10 0 3 13 2 1 0 0 0 10 3 TOT 519 517 212 210 198 196 162 So we now assume that every voter knows this information prior to the actual vote and that everyone decides to vote strategically. They all see that A and B have more than twice the vote of anyone else, and think (fools) that its a race between A and B, so everyone maximizes the difference in their ratings of A and B without changing their preference ordering. The resulting vote: # A B C D E F G 24 10 0 0 0 0 0 0 22 0 10 0 0 0 0 0 14 10 0 10 0 0 0 10 14 0 10 0 10 0 0 10 13 0 10 0 0 10 0 10 13 10 0 0 0 0 10 10 TOT 510 490 140 140 130 130 540 The result: The candidate with the lowest sincere score gets elected! Commentary: This is not a realistic scenario: the ratings of 24 people of 7 alternatives will not be all identical, the use of strategic voting by all concerned is unusual, the availability of sincere totals is hard to explain. The lowest ranked being elected after strategic voting does not look to be a frequent occurrence. In particular, I'm not certain I could come up with an example with fewer than seven alternatives. It's certainly doesn't seem to be as obvious a problem as Warren Smith's DH3 scenario. There shouldn't be any complaint about the strategic result. A majority liked G better than either A or B. Note that Condorcet methods -- I haven't checked them all -- give the sincere win to A or have A and B tied. Borda count goes to A. However, a small change (have the first 46 voters change their rating of G from 0 to 1, and yes, 46% of the voters changing may not be a small change) and G is a Condorcet winner (now sincerely ranked fifth). The real strategic idiots are the voters who like A and B best. If they just kept their high rankings of each other, A or B would still win. Only, how high should they rank their second choice? Too much, and their second choice wins over their first choice, and they need the other guys to rate their second choice higher or their last choice (G) wins. This is starting to sound very much like the awful game that gets played with some strategic Borda voting. Note that the last 54 voters could lock in G by bullet voting G (well, and their favorite). Indeed, G is a possible winner, but not if you look at the sincere tallies. If everyone considers the set of possible winners to be {A,B,G}, the strategic vote changes. Thanks for reading this far. Your comments welcome. Jim Faran ---- election-methods mailing list - see http://electorama.com/em for list info