On Sun, 16 May 2004, Jobst Heitzig wrote: > "Neutrality": Now this is something I did not understand yet. > Quote: > "Neutrality requires that if two problems are such that the ranking > method cannot rank any player [that is, any option! JH] above another, > then the ranking method should still be unable to rank one player above > another when considering the two problems together as a single problem. > And conversely, if two problems are such that in the first one the > ranking method does not rank one player above another, but in the second > problem there are two players that are strictly ordered, then it must be > the case that, when considering the two problems together, there are at > least two players that are ranked one above the other." > At least this seems to apply only in rare cases, where the method fails > to construct any strict ranking at all...
I'd say this means: If you have two elections, A,B,C and D,E,F, if you merge them into A..F, the relative rankings of A:B:C and D:E:F won't change in the merged solution vs the separate solutions. That's what I think they're saying, but I'm not sure why it's really an interesting property of a voting system. > Finally, "negative responsiveness to losses" seems to be the crucial > point implying the fair-bets method: Suppose in some situation, the > method cannot but rank all options equal. Suppose further that now for > each option A some non-negative number lambda(A) is chosen and the > number of voters prefering B to A is multiplied by lambda(A) for each > A,B. Then the axiom requires that the method must now put A above B if > and only if lambda(A)<lambda(B). > > I don't know what the rationale behind this last axiom is, but perhaps > someone can find it. However, I have the feeling that it must be somehow > related to the MinMax rule and to breaking cycles at the weakest link... It sounds to me like a rule for resolving Condorcet ties I once heard. This is confusing because it's saying: "if the method ends up in a tie, the method must resolve ties like this". That's not where I draw the black box of a voting method for comparison. Tie resolution ought to be totally internal and we should just be talking about the final output of the system. -Brian Olson ---- Election-methods mailing list - see http://electorama.com/em for list info