Posted by: Stephen Wildstrom on December 2, 2008
OK, this isn’t about technology, but every year at this time, we need a reminder that there are some issues that that defy all of our efforts, technological or intellectual. Like the selection of the college football teams that will play in the BCS National Championship Game.
This year’s kerfluffle involves the pairing of teams in the Big 12 championship. Missouri won the conference’s northern division but Texas, Texas Tech, and Oklahoma tied for the lead of the southern division. By conference inscrutable rule, the team with the highest standing in the Bowl Championship Series ranking, a combination of human polls and computer algorithms, goes to the title game. That turned out to be Oklahoma by a hair, and Oklahoma is now heavy favored to beat Missouri and advance to the BCS championship.
This has set off the predictable howls that there has to be a better way. But there really isn't, certainly not one that will satisfy everyone. Leaving the choice up to the BCS rankings seems stupid, but there may not be a better way to do it.
More than half a century ago, Stanford University economist Kenneth Arrow proved what is known as Arrow's impossibility theorem: given a choice between more than two candidates and a set of fairness conditions that just about anyone would recognize as reasonable, there is no system for choosing a winner that can be universally recognized as fair. The work won Arrow a Nobel prize in 1972, but people, including economists, election experts, and sportswriters, prefer to act as though it didn't exist. (Arrow's work has always been more honored by mathematicians than by his fellow economists.)
In fact, the Big 12 situation is a classic case of what economists and mathematicians call the intransitivity of choice. All three teams played each other. Texas beat Oklahoma, Oklahoma beat Texas Tech, and Texas Tech beat Texas. In each case, it was the team's only loss. In that situation, there simply is no way to rank the contenders fairly. No matter how much brainpower or computing power we apply to the situation, there is no satisfactory outcome. Those who forget Ken Arrow's work are doomed to pull their hair out, and often in dealing with choices of more consequence than who gets to play in a bowl game.