On 24.6.2011, at 3.47, Paul Kislanko wrote: > Marcus wrote: > Maskin's argumentation doesn't work because > of the following reason: Whether an election > method is good or bad depends on which criteria > it satisfies. > > ---- > > Now, if "good" and "bad" are defined by which criteria methods satisfy, it > seems to me that having introduced "judgement" we need "judges" to define > the "goodness" of each criterion. And if there are more than 2 "judges" to > decide the "goodness" of more than two criteria, there is no unambiguous way > to consolidate the opinions of the "judges."
In addition to defining how important each criterion is we must also estimate how much each method violates some criterion. Since we can not meet all criteria (e.g. being strategy free) and not all interesting criteria at the same time it often makes sense to violate some criteria just a little, so that from practical point of view the method is about as good as if it meth that criterion fully. One bad violation of some key criterion may thus be worse than violating multiple criteria just a little. The number of criteria that some method meets of course has no meaning, only the importance of those criteria has, and maybe also other factors that have no named criterion representing them. > > I think Maskin's "arguent" is actually a really old one - if there's a CW > nobody really has a complaint (though there are pathological cases where the > CW is disliked by a majority of the voters...) This expression s a bit confusing. Majority of the voters may have some other candidates that they prefer to the CW but there is no majority that would prefer one single candidate x to the CW. > and if there's not a CW use > Borda (or Bucklin or ...) considering only the smallest Smith Set. There can be many opinions on if one should always pick the winner from the Smith Set. > > Logically, all we're talking about here is how to order alternatives in > pairwise A>B>C>A loops, right? Well, yes but, in principle there is no need to order the candidates but just pick one winner, and if that loop does not contain all the candidates, then there is also the option to elect the winner from the other candidate. > If we don't like Y=Borda we can start talking > about what "Y" should be if there's a need to have a "Y". Yes, there are also better options. (although Borda may not be too terrible here if we assume that usually we have a CW and people don't care too much who will be elected if there is a tie (=top loop)) Juho ---- Election-Methods mailing list - see http://electorama.com/em for list info
