[EM] Round robin tournament statistics

[fsimmons at pcc.edu]

----- Original Message -----
From: Kristofer Munsterhjelm
Date: Monday, June 27, 2011 1:58 am
Subject: Re: Round robin tournament statistics
To: fsimmons at pcc.edu
Cc: EM

> fsimmons at pcc.edu 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?