Transitive Property

A relation R is transitive if, for a set X, R(a, b) and R(b, c) implies R(a, c) for all a, b, c in X. In quizbowl, a team A is held to have a transitive win over team B at a tournament if the relation “beat” is taken to be transitive and “team A beat team B” is true. For example, every team at 2025 ACF Nationals transitively beat the eventual champion Stanford.

Of course, beating a team is clearly not transitive in the ordinary sense of the word “beat,” since it is possible for A to have a transitive win over B without ever playing B. However, maybe one would like to think that beating a team means that you are better than them and also that being “better than” another team is transitive. This would then still imply, in tournaments where teams split games or there is a circle of death, that there are teams who are better than themselves. Whether or not this is obviously false is left for the reader to decide.

Quizbowl players often joke about transitively (or directly) beating/being better than teams that placed higher than them/won the tournament. Albert Zhang created an interactive website based on this idea.