“Overcoming Incentive Constraints by Linking Decisions,” M. Jackson and H. Sonnenschein (2007)

Classical economics is concerned with constrained decisionmaking when the constraints are technological. Modern economics is concerned with constrained decisionmaking given both technological and incentive constraints: that is, people have interests, and can lie, and any “optimal” policy must take this into account. That line of reasoning is, I think, what really separated economics from other social sciences. The problem is that, with incentive constraints, many things are impossible: voting (Arrow, Gibbard-Satterthwaite), bilateral trade (Myerson-Satterthwaite) and on and on.

In this 2007 Econometrica (coauthored by the legendary Sonnenschein, who has long been in administration at U Chicago and who I did not realize was still doing active research), the authors point out that linking decisions can help alleviate incentive compatibility problems. Imagine that agents regularly vote on bills, and that all bills have preferences uniformly distributed on [-2,-1,1,2], and that this is common knowledge. With two voters, in a one-stage game, there is clearly no incentive compatible mechanism: everyone will claim to have “strong preferences” (-2 or 2). But imagine we vote many times, and each player is given a “budget” of votes for -2,-1,1,2 corresponding to the known distribution (.25 for each). Then lying by misrepresenting “weak” (-1 or 1) preferences as strong will harm my own future self. Extending this example, it turns out that with some technical conditions, the Pareto optimal outcome in terms of whatever social choice function you like can be achieved by linking enough decisions together. The proof works since the Law of Large Numbers means the sample distribution of preferences approximates the true distribution as the number of decisions increases, and if that is the case, then misrepresenting preferences now will only hurt your own self later given the “budget”.

This result is similar to a recent paper by Casella which showed how allowing members of a committee (an EU parliament, in his case) to “store votes” leads to Pareto improvements, since each agent will only vote when they have strong preferences; the Casella result is not as theoretically interesting, but it does give a mechanism in the same vein that has real world applications. Also, for the mathematically-inclined, the proofs in Jackson-Sonnenschein look in many ways like the Debreu-Scarf result on the core of an economy.

http://home.uchicago.edu/~hfsonnen/download/NotesandCommentsOvercoming.pdf

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