Condorcet's Committee

Reality is so much more fun when it illustrates a good theory.

On Thursday afternoon, I was attending a meeting of the General Education Task Force (GETF), whose purpose is to create a reformed General Education program for the university. A worthy task, but also a tedious and frustrating one. As we debated a particular aspect of the program relating to the degree of disciplinary breadth required of students, it became clear we had three main options. Option A was the most restrictive of students’ GE choices, option C the least restrictive, and B somewhere in between. The proposals had other characteristics, aside from their restrictiveness, that mattered to some members of the committee. I proposed a straw vote. The chairperson allowed people to vote for more than one option, and I noted that some people supported both A and B, and (as I recall) others supported both B and C.

I had a sneaking suspicion that something more intriguing was going on, so I suggested that we ought to have three pairwise votes – A vs. B, B vs. C, and A vs. C. The votes were taken, and it was just as I’d suspected: A beat B, B beat C, and C beat A. We had a genuine Condorcet paradox!

At this point, I realized that, unless further discussion altered someone’s preferences, any outcome we chose would be arbitrary. We could choose a voting mechanism if we liked, and the voting mechanism would select a winner, but in no way would it reveal a “general will” or consensus of the committee. The outcome would depend crucially on who was most successful in affecting the voting rule.

Ultimately, someone proposed a run-off vote: we’d vote on all three proposals, throw out the one with the least votes, and then have a run-off between the top two. This assured that the option that was the first choice of the fewest people – which happened to be option B – would lose. The winner was option C.

I’m not sure, but I think some committee members believed the outcome actually proved something – say, that C was somehow the “committee’s” favored option. To demonstrate this was not so, I was tempted to say we should now vote between C and B, “just to be sure we’ve got the best option.” B would have won, assuming preferences remained unchanged. But I refrained, because I realized that even though C was an arbitrary choice, it was no less arbitrary than any other choice we could have made. So I remained silent, satisfied just to have seen Condorcet in action. Ain’t democracy grand?