Bicker at Princeton

Vikram Rao writes about recent changes in the matching process of students to eating clubs at Princeton:

Professor Roth,

I'm a fan of your blog and recently came across an event that you might find interesting. I studied as an undergrad at Princeton, which is known for its "eating clubs" - similar to frats or sororities, but they are co-ed, serve meals, and function as daytime study and lounge spaces. Anyway, admission to half the eating clubs is by "sign-in" where a lottery occurs if too many students try to sign in. The other half of the clubs have a process called "bicker" - a traditional matching process where prospective members show up for a few days of events and then members discuss and vote on each prospective member.

Recently, a few of the clubs decided to allow prospective members to bicker two clubs instead of one (http://www.dailyprincetonian.com/2012/11/08/31741/). Students rank their clubs and then show up to events for both; they are NOT allowed to indicate equal preference for both clubs (this fact isn't in the article but I know from friends). The interesting situation arises when a student is accepted at both clubs - the matching algorithm will always default to the student's preference for club (so if I get into club A and B and said I preferred B beforehand, I will be placed in B). 

On the face of things, this sounds unremarkable. However, I think this matching market has an interesting wrinkle for students who are admitted to two clubs. 

Following the "bicker" process, prospective members are ranked by each club. Prospective members aren't supposed to find out how they did at bicker, but as you might imagine gossip spreads and the people who were ranked the highest often find out about it. Those who did well feel like they belong and are more excited about the club. 

Given the opportunity to bicker more than one club, I suspect that some students will be indifferent or close to indifferent between two clubs. But they will be forced to rank the two clubs. Following the bicker process, it might turn out that they did much better at their #2 ranked club. But the match will sort them into their #1 ranked club. Given the aforementioned desire to “belong”, it’s possible that this could lead to instability in the match (Student: “Now that I know I did so much better at club C bicker, I wish I ranked it ahead of club D!”). Perhaps a way to solve this is to let students indicate indifference between the two clubs beforehand and then have the algorithm place them in the club that ranked them higher.

This situation seems to differ from say a medical residency or a job where most people probably want their best possible job regardless of how well their application was perceived by those doing the evaluation. With a social group like this, you don’t just want to get in but might also want to feel “wanted” in an ongoing way.