----- Original Message ----- From: Kristofer Munsterhjelm Date: Monday, June 27, 2011 1:58 am Subject: Re: Round robin tournament statistics To: [email protected] Cc: EM
> [email protected] wrote: > > > > ----- Original Message ----- > > From: Kristofer Munsterhjelm > > Date: Saturday, June 25, 2011 2:26 pm > > Subject: Round robin tournament statistics > > To: EM > > Cc: Forest W Simmons > > > > >> It gets more difficult when one takes ties into account, > though. > >> For most games, no pair is exactly tied in the long run, but > one > >> could imagine a game where if both players cooperate, there's > >> always a tie (such as two players in chess agreeing to always > do a > >> grandmaster draw, based on tit-for-tat reasoning). Then a > long run > >> of ties would in itself be significant: it means that neither > >> player is (or chooses to be) any better than the other. Just > >> eliminating ties from consideration, as you did in the winner > >> calculation, wouldn't work because it could take a really > long time > >> before a non-tie result is granted. > >> > > > > That's where the "Independent Identically Distributed" proviso > comes in. If there is any kind of mutual > > strategy, this condition cannot hold. > > It doesn't have to be strategy. I've been considering this > problem in > the setting of coevolutionary algorithms. Say, for instance, > you're > trying to make a game AI in a shooter. Then, very early "random" > programs might not know to shoot at each other at all, which > means > nobody ever dies, and so it's always a tie. > > > What I was more concerned with, ultimately, was how equal > rankings would affect the significance of the > > defeat. In other words, suppose there are 100 ballots, and > W=40 support the winner, L=10 support the > > loser, and the other fifty rank them equally or truncate them > both. Does this 40 to 10 defeat have the > > same significance as a 40 to 10 defeat in which there were > only fifty ballots total? > > > > According to the above model (with the independent identical > distribution condition) the answer is yes. > > > > That makes things nice for comparing pairwise defeat strengths > in the case of sincere rankings. > > > > As I mentioned before, these sincere rankings are most likely > in the case of informal polls before the > > actual election. > > I also imagine it would be useful in places where it's hard to > strategize or the context means there won't be any strategy. > Such > examples might be computers in a redundant system voting about > an > observation under uncertainty (the "strategy" will be a random > distortion) or actual round robin tournaments (where engineering > a > Condorcet cycle based on just one's own matchups would be quite hard). > Or how about in the context of ranking websites for search engine hits? ---- Election-Methods mailing list - see http://electorama.com/em for list info
