Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process
Research Seminars: Virtual Market Design SeminarThe paper presented in this Virtual Market Design Seminar considers the problem of aggregating individual preferences over alternatives into a social ranking. A key feature of the problems that the authors consider—and the one that allows them to obtain positive results, in contrast to negative results such as Arrow’s Impossibility Theorem—is that the alternatives to be ranked are outcomes of a competitive process. Examples include rankings of colleges or academic journals. The foundation of the ranking method is that alternatives that agents rank higher than the one they receive (and thus have been rejected by) should also be ranked higher in the aggregate ranking. The paper introduces axioms to formalize this idea, and call any ranking that satisfies our axioms a desirable ranking. The paper shows that as the market grows large, any desirable ranking coincides with the true underlying ranking of colleges by quality. Last, the authors provide an algorithm for constructing desirable rankings, and show that the outcome of this algorithm is the unique ranking of the colleges that satisfy our axioms.
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