Dear Ernie! you wrote: > Hi Jobst, > > On Apr 24, 2004, at 5:49 AM, Jobst Heitzig wrote: > >> Def. INDEPENDENCE OF STRONGLY DOMINATED ALTERNATIVES (ISDA): >> Removing a strongly dominated alternative must not change the winner. >> X is STRONGLY DOMINATED by an alternative Y if >> (i) Y beats X >> and, for all Z distinct from X,Y: >> (ii) if Z beats Y, Z beats X even stronger, >> (iii) if Z beats X, Y beats X even stronger, >> (iv) if X beats Z, Y beats Z even stronger, and >> (v) if Y beats Z, Y beats X even stronger. >> >> In the general case, Pareto-dominated alternatives are also strongly >> dominated but not vice versa, hence ISDA is then stronger than IPDA. As >> Steve already pointed out for Pareto-dominated alternatives, such >> strongly dominated alternatives might be easily be found by a losing >> party and be added strategically to change the winner, which should not >> be possible. > > > Very impressive. Just to make sure I understand, are you effectively > saying that ISDA means that removing -or- adding an SDA shouldn't change > the results?
I think so -- isn't that the same proposition? > Also - I didn't know this, perhaps you did - there's now a very nice > Wiki writeup on MAM: > > http://en.wikipedia.org/wiki/Maximize_Affirmed_Majorities > > I'd love to see a similar article on the River; in fact, if you write > it, I'd be happy to help Wikify it, if that's a barrier. Thank you very much for your encouragement. Anyway, I don't think the River method is elaborated enough yet to be described "officially" in a Wiki -- I'm sure it needs some weeks of discussion to find out its advantages and disadvantages. For example, an open question is how to deal with same-size majorities -- there are many possibilities: (a) Use a tiebreaker as in MAM or MMV (which would at least ensure monotonicity), or (b) determine all lexicographically maximal trees or almost-trees and choose one uniformly at random, or (c) determine all destinations of lexicographically maximal trees or almost-trees and choose one uniformly at random, or (d) simulate the interactive version by successively choosing statements with a probability proportional to the corresponding majority, and so on... Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
