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Separability and aggregation of equivalence relations

Author

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  • 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. 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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    3. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    4. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    5. 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.
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    7. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
    8. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2696-2705.

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    JEL classification:

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

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