In this case, the issue seems to come down to whether we count the preferences of the dead. If we don’t, then surely no harm is done by tomb raiding. To me, it’s clear that the preferences of the dead should not count, but I’m aware that what seems clear to me does not always seem clear to everybody.

Here’s one way to do this: Assume each team has a numerical “strength”, and that the strength of a team is proportional to the sum of the strengths of the teams that it beats.

For example, say teams A, B and C have strengths x, y and z. If team A beats teams B and C, team B beats team C, and team C beats team A, then we conclude that for some constant K, x=K(y+z), y=Kz, z=Kx. We can solve these equations to get (approximately) x=1.3, y=.75, z=1, K=.75. So A ranks first (with a score of 1.3), C ranks second (with a 1) and B ranks third (with a .75).

With more teams, the equations get more complicated and the rankings get less obvious but the same method applies.

This is essentially how Google ranks the importance of web pages: Receiving a link from a page counts as “beating” that page, and your page is assumed to have an importance proportional to the sum of the importances of the pages that it “beats”. This gives a massive list of equations (one for each page on the web) that you can then solve to get the rankings.

The arguement is “well if you do a playoff you better not be the 9th ranked team if they take the top 8 or the 17th ranked team if top 16 etc.” I say that’s phooey and would be way more fair. This year there are 4 unbeaten teams and only two get to go to the nat’l championship game!