At 03:51 PM 10/25/2006, Juho wrote: >On Oct 25, 2006, at 7:07 , Abd ul-Rahman Lomax wrote: > > And methods which ignore strength of preference cannot maximize > > social utility. > > And if strength of preference is considered, there goes the > > Majority Criterion.... > >I at least made a try few mails back on the list with "Ranked >Preferences".
Tried what? To satisfy the Majority Criterion while allowing preference strength to influence the outcome? I don't think it is possible. However, I found the description of "Ranked Preferences" to be incomprehensible. It's *complicated*. I suspect that there might be a way of expressing it which is much simpler, or maybe not. If not, forget about it. If I can't figure it out with a few minutes of focused attention, the public will *never* go for it. > I don't claim that all the criteria are fulfilled but >some basic cases work. Votes 55: A>B>>C, 45: B>>A>C elect A (the >majority favourite) although the B supporters strongly disliked her. Let's express this in Range terms to see what it might mean. I'll assume that there are three candidates total, A, B, and C. What has been expressed above could simply be represented by assuming that there are four ranks. A preference gap of two ranks is expressed by ">>". So the range ratings (Range 0-3) are: 55: A:3 B:2 C:0 45: A:1 B:3 C:0 Hey, why did C even bother to run? Perhaps to cause the election of B.... Range can do that, it is not immune to the influence of "irrelevant" candidate entries, if they distort the matrix. However, the remedy for this is in the hands of the voters: it is to bottom rate more than one candidate. A voter might bottom rate a whole range of candidates. If this is recommended practice (not just bullet-voting), then Range would not be vulnerable to strategic presentation of really bad candidates.... They would not raise the rating of moderately bad candidates.... Anyway, this election, as stated, comes out to be (totals) A: 3 * 55 + 45 = 210 B: 2 * 55 + 3 * 45 = 245 B wins. B wins even more handily if the >> represents a greater gap. >Strong votes however have power in other circumstances since votes >40: A>>C>B, 40: B>>C>A, 20: C don't elect the Condorcet winner C >since A and B supporters strongly dislike her. Social utility is >maybe not yet maximized but maybe improved?? Unclear. Badly polarized vote patterns often create weird results. I'd suggest coming up with a clearer explanation, with calculation examples of the proposed method. In any case, the Majority Criterion is doomed for any method which *considers* preference strength, no method that allows preference strength to affect the results can satisfy the Majority Criterion. Yet it is quite clear that it is necessary to consider preference strength to get optimal election results, or else casual or trivial preferences carry the same weight as strong preferences (in some of the examples we have given, these "preferences" are actually "needs.") ---- election-methods mailing list - see http://electorama.com/em for list info
