On Mon, 03 Jan 2005 00:26:05 +1030, Chris Benham <[EMAIL PROTECTED]> wrote: > Florian Legyel asked me (Sat.Jan1): > > >What is the sensible and fair argument linking the minimization of > >Bayesian regret by range voting with the emotional states of voters? > > > CB: I could perhaps have omitted the word "Bayesian", because that > just refers to "averaged over a vast number of > randomized elections".
It's better to be more specific about what is being averaged: WD Smith's simulations assign, for each voter and candidate, the utility a given candidate has for that voter. This is not an "emotion"--it is, in Smith's simulation, a real number between 0 and 1. The "Baysean regret" assigned by a voter to an election is the difference between the utility assigned to the winning candidate by that voter and his preferred candidate; these differences are averaged in the simulations of each voting method. > Ok, suppose there are two candidates and three voters, and the voting > method is Range Voting > using the scale 0-100. All three voters are completely sincere. > > Voters 1 and 2 both prefer candidate A to candidate B, but not by much > and they are not very impressed by either. They > vote A27, B25. Voter 3, on the other hand, is infatuated with B and > thinks that A is by comparison terrible, so votes > A2, B98. This is how W.D Smith measures "regret" in his simulations. Could you point out in the simulations where this is? I see no mention of the utility assignments in WD Smith's program in this account. > Range Voting would just add up the points and elect B, minimizing > "regret". Voter 3 over-ruled the other two voters, by > being more emotional. "Regret" is an emotion, isn't it? This seems to sidestep the technical definition of Bayesian regret with extra-mathematical psychological considerations. The issue is not whether regret is an emotion. Bayesian regret is a term for the difference in utility a hypothetical voter would assign to two candidates. Smith's simulation makes the assumption that voters make such utility assignments. He also allows voters to be ignorant of the "real" utility a candidate has, by introducing a random deviation from the "true" value. A question is whether such assumptions are sociologically and politically substantive. Voter 3's > greater self-quantified potential "regretfulness" (96 points > of it) over-ruled the other two voters' total of 4 points of > potential regret. > > That is why I say that the assertion by Range Voter advocates that > "minimizing...regret" is more important than majority > rule is tantamount to saying that more emotional voters should have more > power than less emotional voters. > > Chris Benham I don't believe WD Smith ever asserted that minimizing Bayesian regret is more important than majority rule. His statement was that range voting minimizes Bayesian regret--it's a statement about a simulation of voting methods assuming some kind of a priori assignment of utilities each voter in an election assigns to a list of candidates. The three-voter example you give does not involve a minimization over a distribution of candidate utility assignments by the voters. Perhaps it would be a good idea to run the simulation with three voters. FL ---- Election-methods mailing list - see http://electorama.com/em for list info
