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Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process

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  • Thayer Morrill
  • Peter Troyan

Abstract

We consider the problem of aggregating individual preferences over alternatives into a social ranking. A key feature of the problems that we consider, and the one that allows us 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 our ranking method is that alternatives that an agent desires, those that they have been rejected by, should be ranked higher than the one they receive. We provide a mechanism to produce a social ranking given any preference profile and outcome assignment, and characterize this ranking as the unique one that satisfies certain desirable axioms.

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  • Thayer Morrill & Peter Troyan, 2022. "Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process," Papers 2205.11684, arXiv.org.
    • Handle: RePEc:arx:papers:2205.11684
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    References listed on IDEAS

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    1. Griffith, Amanda & Rask, Kevin, 2007. "The influence of the US News and World Report collegiate rankings on the matriculation decision of high-ability students: 1995-2004," Economics of Education Review, Elsevier, vol. 26(2), pages 244-255, April.
    2. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    3. Christopher N. Avery & Mark E. Glickman & Caroline M. Hoxby & Andrew Metrick, 2013. "A Revealed Preference Ranking of U.S. Colleges and Universities," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 425-467.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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