The whole Elo rating system is based on that assumption of transitivity. (More precisely it's based on the hypothesis that a one-dimensional parameter is enough to describe some player's strength, hence the parameters of all players can be totally ordered.)
Whether it is true is another whole question of course, but seeing how robust the rating system is, I would tend to think it has robust foundations too. My opinion, of course.
Yes, I think the rating system is quite reliable. The criticism against it often depends on single results being overestimated as a sign that the rating system is "wrong". If Carlsen had been ill in November or had the worst week of his life most people would probably have interpreted that as Anand being the best player in the world, not as if Carlsen had one horrible result.
The whole Elo rating system is based on that assumption of transitivity. (More precisely it's based on the hypothesis that a one-dimensional parameter is enough to describe some player's strength, hence the parameters of all players can be totally ordered.)
Whether it is true is another whole question of course, but seeing how robust the rating system is, I would tend to think it has robust foundations too. My opinion, of course.
@anyone quoting triplets of players with nontransitive scores : any three players of roughly equal level are likely to exhibit such behaviour. It's just statistics.
For instance, I just organized a heads-or-tails world championship. A won to B, B to C and C to A, as it would happen 1/8th of the time (1/4th if you allow the circle to run in the other direction). Does it mean anything deep about the game of heads-and-tails and the style of players ?