Range voting

The “range voting” system is as follows. In a ccandidate election, you select a vector of c real numbers, each of absolute value ≤ 1, as your vote. E.g. you could vote (+1,−1, +.3,−.9, +1) in a 5-candidate election. The vote-vectors are summed to get a cvector ~x and the winner is the i such that xi is maximum. Previously the area of voting systems lay under the dark cloud of “impossibility theorems” showing that no voting system can satisfy certain seemingly reasonable sets of axioms. But I now prove theorems advancing the thesis that range voting is uniquely best among all possible “Compact-set based, One time, Additive, Fair” (COAF) voting systems in the limit of a large number of voters. (“Best” here roughly means that each voter has both incentive and opportunity to provide more information about more candidates in his vote than in any other COAF system; there are quantities uniquely maximized by range voting.) I then describe a utility-based Monte Carlo comparison of 31 different voting systems. The conclusion of this experimental study is that range voting has smaller Bayesian regret than all other systems tried, both for honest and for strategic voters for any of 6 utility generation methods and several models of voter knowledge. Roughly: range voting entails 3-10 times less regret than plurality voting for honest, and 2.3-3.0 times less for strategic, voters. Strategic plurality voting in turn entails 1.5-2.5 times less regret than simply picking a winner randomly. All previous such studies were much smaller and got inconclusive results, probably because none of them had included