As the BCS Championship game is about to start: Most people are saying that Florida or Oklahoma will emerge from tonight’s game as college football’s number 1 team, though Utah has a shot if neither looks too impressive. Texas fans are cheering for Oklahoma, partly out of Big 12 loyalty, partly out of desire to have beaten the #1 team, and partly because of the following argument: Oklahoma would be #1; but Texas beat Oklahoma 45-35; so, Texas should really be #1.
There’s some plausibility to that argument. But the underlying transitivity principle would also validate this argument for a championship for New Hampshire:
The Wildcats beat Army, which beat Louisiana Tech, which beat Mississippi State, which beat Vanderbilt, which beat Mississippi, which handed the No. 1 Gators their only loss.
UPDATE: Now that Florida has won, we need to take that “six degrees of separation” argument more seriously. Florida lost to Mississippi, who lost to Vanderbilt, who lost to Mississippi State, who lost to Louisiana Tech, who lost to Army, who lost to New Hampshire. But New Hampshire lost to Northern Iowa, who lost to Richmond! So it’s Richmond who should claim the championship, not just of its own division, but of 1-A! Of course, Richmond lost to UVa, and UVa lost to seven teams, so….