Sunday, November 7, 2010

What Does Transitivity Mean?

Apparently the football polls don't know: Missouri beat Oklahoma 36-27 (and the game wasn't that close). Missouri also beat Texas A&M 30-9 (at A&M). Plus Texas A&M beat Oklahoma 33-19. However, the polls rank Oklahoma above Missouri. Somebody's not paying attention.

Transitivty: a relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third. I.e. Missouri>Texas A&M, Texas A&M>Oklahoma, thus Missouri>Oklahoma. In this case we also have the absolute: Missouri>>Oklahoma. There is no justification whatsoever for the ranking order in the polls. At least the computers like Missouri better. The Human polls are looking increasingly like they make no sense whatsoever.

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