speculation about ratings and playing strength

This line of thought originated in a discussion on rec.games.go about the possibility of improving the IGS rating system by finding some absolute reference for playing strength: based on either God's playing strength at one extreme; or the totally random move generator at the other.

It's Interesting idea, but I think the idea of absolute ratings is fundamentally flawed. Absolute ratings would have to be transitive: A is better than B is better than C implies that A is better than C.

I think would be pretty easy to demonstrate that transitivity depends on qualitative aspects of the players' skills. One could construct a set of players, each using a different simple strategy, such that A defeats B, B defeats C, and C defeats A.

Given the above construction, it would follow that any rating scheme can exhibit anomolies. If you think about it, it makes sense from that all players are flawed in their own peculiar ways, and that the flaws are not comparable in any simplistic way.

Meanwhile, in the real world

This line of thinking leads me wonder if this phenomenon is a factor in the odd distribution of titles in the professional world. One would expect that if the competition for titles were completely open and fair, then the one "best" player would tend to hold all titles at once. Sometimes that does seem to be the case, but often certain players seem to have "locks" on some titles and "jinxes" against others. It could be that the tournament rules, which determine who will play whom, based on the underlying assumption of transitive playing strength, don't select the best challenger.