Soldiers of Fortune goes to Hollywood

October 12, 2017
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There are six identical men, who must choose one of them to do an unpleasant job. They could hold an auction and pay one of them to volunteer to do the job. But if they have diminishing marginal utility of consumption, they will prefer instead to roll a die to decide which one of them does the job. Their expected utility is higher. If the job is unpleasant because it has a risk of death, then state-contingent preferences (the marginal utility of consumption when dead is zero) strengthen the argument for a lottery.

That’s the intuition behind a paper I read 25 years ago, about lotteries and the draft for the Confederate Army. I think the title was “Soldiers of Fortune”, but I don’t remember the author, and I can’t find it on the internet. Sorry.

Now imagine that a seventh man controls the die, and can offer deals to the other six. He can collect rents in exchange for tilting the die. But there is a limit to how much rent he can collect, or the six will instead auction the job among themselves.

Now change the model, reversing the sign, so the job that one of them will do becomes pleasant. One of them will become a movie star. With diminishing marginal utility of consumption, they will prefer to roll a die to decide who gets to be the star. And with state-contingent preferences (being a star increases the marginal utility of consumption) that strengthens the argument for a lottery.

And again, if a seventh man controls the die, he can collect rents. But there’s a difference, because in this case the seventh man need only make a deal with one of the six, not with five of the six. If the other five don’t know about the secret deal, they won’t revert to the auction.

[Trying to answer a question raised by Steve Randy Waldman’s tweet.]

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