Hi Forest, --- En date de : Lun 2.5.11, [email protected] <[email protected]> a écrit : > In liberal arts mathematics text > books Arrow's impossibility theorem is usually > quoted as saying that no election method can simultaneously > satisfy (1) > neutrality, (2) anonymity, (3) decisiveness (4) monotonicty > (5) the majority > criterion (6) the Condorcet Criterion, and (7) the > Independence from Irrelevant > Alternatives Criterion (the IIAC), as though all of these > requirements were > equally to blame for the incompatibility,
That is the longest list I've ever seen. I'm used to seeing 4+5+6 replaced by Pareto perhaps. Condorcet would already imply majority, unless this is supposed to be mutual majority. > when in reality > conditions one through > six are perfectly compatible with each other, but condition > seven is not even > compatible with the existence of a Condorcet cycle. Well, we would probably expect "all properties but one" to be compatible. Drop out #7 and you can have a method. But drop out #6 and you still don't have a method. It's clear, as you write, that IIA isn't compatible with Condorcet. It's not compatible with much of anything. I take that to be the point of Arrow: If you want IIA you have to do some drastic things. If I could have IIA (and for real, not on a technicality) I would certainly want it... Kevin ---- Election-Methods mailing list - see http://electorama.com/em for list info
