Monday, November 7, 2011

What do policy makers want from a market design? And what would be the consequences of giving it to them? Clayton Featherstone on rank efficiency.

A surprising variety of allocation mechanisms, such as those used for school choice, ask participants to rank-order the alternatives; i.e. to indicate their first choice, second, third, and so forth. Not surprisingly, one thing that policy makers want to know about any proposed mechanism is how many people will receive their first choice, second, third, and so on.

Clayton Featherstone is a market designer who already has an unusual amount of experience in designing and implementing choice mechanisms. (If you recently got an assignment from Teach for America, or were assigned to a country for your global immersion requirement at HBS, you've benefited from his work.) His job market paper is an investigation of the properties of "rank efficient" mechanisms, which are designed to produce outcomes whose distribution of ranks can't be stochastically dominated:
Rank Efficiency: Investigating a Widespread Ordinal Welfare Criterion 

 Here's the Abstract: "Many institutions that allocate scarce goods based on rank-order preferences gauge the success of their assignments by looking at rank distributions, that is, at how many participants get their first choice, how many get their second choice, and so on. For example, San Francisco Unified School District, Teach for America, and Harvard Business School all evaluate assignments in this way. Preferences over rank distributions capture the practical (but non-Paretian) intuition that hurting one agent to help ten might be desirable. Motivated by this, call an assignment rank efficient if its rank distribution cannot feasibly be stochastically dominated. Rank efficient mechanisms are simple linear programs that can be solved either by a computer or through a sequential improvement process where at each step, the policy-maker executes a potentially non-Pareto-improving trade cycle. Both methods are used in the field. Preference data from Featherstone and Roth (2011)'s study of a strategy-proof match shows that if agents were to truthfully reveal their preferences, a rank efficient mechanism could significantly outperform alternatives like random serial dictatorship and the probabilistic serial mechanism. Rank efficiency also dovetails nicely with previous literature: it is a refinement of ordinal efficiency (and hence of ex post efficiency). Although rank efficiency is theoretically incompatible with strategy-proofness, rank efficient mechanisms can admit a truth-telling equilibrium in low information environments. Finally, a competitive equilibrium mechanism like that of Hylland and Zeckhauser (1979) generates a straightforward generalization of rank efficiency and sheds light on how rank efficiency interfaces with fairness considerations."

Clayton’s paper also solves an empirical puzzle about those matching mechanisms that we see “in the wild”. The theory literature has paid a good deal of attention to ordinally efficient mechanisms, as first described by Bogomolnaia and Moulin, who showed that ordinal efficiency can be obtained through a class of “simultaneous eating” mechanisms. But, despite the appeal of ordinal efficiency, no one has ever reported that such mechanisms have been observed in use. Clayton shows that a class of linear programming mechanisms  and an equivalent class of incremental improvement mechanisms that we do observe in practice produce rank efficient outcomes. So, he shows, there are ordinally efficient mechanisms in use; just not those that were previously known to produce ordinally efficient outcomes before he showed that they produced rank efficient outcomes and that rank efficiency implies ordinal efficiency.

Clayton is an unusually experienced market designer whose field experience motivates novel theoretical insights. He's also a talented experimenter who studies market design issues in the lab. He's a Stanford Ph.D. who is finishing up a two-year postdoc with me at Harvard. His other papers are on his Stanford job market page; you could hire him this year.

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