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Separability and aggregation of equivalence relations

Author

Listed:
  • Dinko Dimitrov

    (University of Munich)

  • Thierry Marchant

    (Ghent University)

  • Debasis Mishra

    (Indian Statistical Institute, New Delhi)

Abstract
We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto+ and Pareto-. If we drop Pareto-, then conjunctive separability and Pareto+ characterize the family of meet aggregators along with a trivial aggregator

Suggested Citation

  • Dinko Dimitrov & Thierry Marchant & Debasis Mishra, 2009. "Separability and aggregation of equivalence relations," Discussion Papers 09-06, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:09-06
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    References listed on IDEAS

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    5. Nicolas, Houy, 2007. ""I want to be a J!": Liberalism in group identification problems," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 59-70, July.
    6. Murat Çengelci & M. Sanver, 2010. "Simple Collective Identity Functions," Theory and Decision, Springer, vol. 68(4), pages 417-443, April.
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    Cited by:

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    4. Klaus Nehring & Marcus Pivato & Clemens Puppe, 2016. "Unanimity overruled: Majority voting and the burden of history," Journal of Theoretical Politics, , vol. 28(4), pages 552-597, October.
    5. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    6. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
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    8. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Christopher Chambers & Alan Miller, 2011. "Rules for aggregating information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(1), pages 75-82, January.
    10. Craven, John, 2024. "Aggregation of ranked categories," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 27-33.

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • D0 - Microeconomics - - General

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