Thanks to Jobst for clarifying the conditions under which various kinds of individual and social utilities can be justified.
A most important idea is that for social utility the average of two lotteries could have more utility than either lottery separately because of the social value of having utility spread out instead of concentrated. This insight is especially important for Western democracies in which great pains have been taken to caulk up all of the trickle down leaks. As Jobst noted, this fact makes the usual plain average rating method of range voting somewhat inappropriate for our democracies. He has in fact justified the use of the Gini score which is a much more appropriate kind of weighted average. In the deterministic case this just means that we should use range ballots and elect the candidate with the highest Gini score. Of course, strategic voters would still vote at the range extremes, as in approval strategy, though the pressure to do so would be less. To make the lottery version computationally tractable, one would have to limit the number of lotteries to certain standard combinations of the candidates as well as any lotteries that are specifically nominated before some cutoff date. Indirectly through their range ballots the voters' individual utilities for the various lotteries are inferred. Then the Gini scores for those lotteries yield their respective social utilities. Jobst and I happen to like lotteries as instruments of fairness and as devices for foiling manipulation. But it should be pointed out, that although his essay gives lotteries a central role, in that context it is primarily a theoretical tool for showing the existence of meaningful individual and social utilities in the presence of certain hypotheses concerning binary preferences between lotteries. I hope that these rremarks are helpful. Forest ---- election-methods mailing list - see http://electorama.com/em for list info
