It drives me crazy when lotteries are not incentive compatible (http://en.wikipedia.org/wiki/Incentive_compatibility). For example the Stanford housing lottery is crazy. They assign everyone to their first choice until houses are full and then assign everyone to their second choice and so on. So if you put a popular house first you are taking a big risk. Really stupid.
I was talking to some economist at Harvard who came to Yahoo who convinced the Boston Public Schools so that they used an incentive compatible lottery for school assignments. The lottery is a little harder to explain, but the big benefit is that less informed or sophisticated families don't end up with worse housing. What a great application of game theory.
http://www.people.fas.harvard.edu/~ppathak/papers/boston.pdf
Also, if any nerds are still reading, that Levitt paper on penalty kicks approximating the mixed strategy equilibrium is really interesting: http://pricetheory.uchicago.edu/levitt/Papers/ChiapporiGrosecloseLevitt2002.pdf . I'm not sure if his assumptions are correct, but the fact that kickers actually kick to their weak side more often than their strong side is pretty interesting evidence that game theory can explain some non obvious things.
2 comments:
That's not actually how the Stanford housing lottery works. The person with number 1 gets their first choice, then the person with number 2 gets their first, then number 3, and so on, until a house is full, at which point they go on to someones second choice, etc.
Everyone is always confused about how it works, because the algorithm for determining the results is:
1. Start with everyone as "unassigned"
2. Assign everyone who is unassigned to their #1 choice
3. In the overbooked houses, kick out the people with the lowest numbers and put them in the "unassigned" list. Also remove the house from their preference list.
4. If no one is unassigned, stop. Otherwise, go to step 2.
Actually, I'm not sure what the "stop" criterion is, and it's possible that the algorithm stops early and doesn't give the true solution. Still, I think the risk of putting a popular house as #1 is pretty negligible.
Still that's not incentive compatible. Especially because the houses are small compared to the pool of people, by your algorithm its very dangerous to put your true first choice.
Assume everyone has the same preference ordering and everyone knows what house they can get. You put your true ordering, everyone else puts optimal ordering. So everyone gets assigned their first choice and you get the worst house (assuming you don't get the best house). This seems pretty bad.
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