On Fri, Jan 30, 2009 at 10:09 PM, Juho Laatu <[email protected]> wrote: > I don't know what the voter would > think. Maybe some voters think that > the two alternatives are equal. > Maybe most prefer the latter > alternative. > > In any case the first alternative > may lead sooner to situations where > the representatives make different > decisions than the voters would.
I think if the method complies with the proportionality for solid coalitions criterion, then it would tend to give a PR result. One option would be to have 2 measures, one measures how PR the method is and one measures the average utility. Another option would be to increase the weight for unhappy people when working out the average. For example, the most unhappy person would be given a weighting of 2 and the happiest person would be given a weighting of 1 (and the rest would be given a weighting based on the position of the voter between the 2). This would make it harder to offset one group of people against another. The real problem is how to do it in a way that doesn't tend towards bias. At least in a single seat election, summing the utility is a pretty unbiased method. PAV uses the rule 1+1/3+1/5+1/7 + ... (i.e. terms = number of approved candidates elected) However, it doesn't just average the results. If one of your candidates are elected, then it counts as full strength, but the 2nd candidates counts at 1/3 of that strength. The voter's happiness is 2 units, but it only counts as 1.33 units. Effectively, that voter's happiness is deweighted by 33%. RRV doesn't quite work that way, but it gives the same kind of result to sequential PAV. Anyway, maybe the system could be something like For each possible winning set - work out the average utility for each voter of all the candidates in the winning set - sort the voters in order of their happiness - give each voter a weight dependent on the position in the ordering - the happiness for that result is equal to the average happiness using the above weightings If the weighting was 1 no matter what, then it wouldn't be a PR method. I wonder if there is a weighting that would achieve Droop proportionality. If a group of voters were to vote max for 1 candidate, and min for all the rest, I wonder is there a weighting function that will guarantee that that candidate will be in the best winning circle. ---- Election-Methods mailing list - see http://electorama.com/em for list info
