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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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    1. Dimitrov, Dinko & Puppe, Clemens, 2011. "Non-bossy social classification," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 162-165.
    2. Dean Neumann & Victor Norton, 1986. "Clustering and isolation in the consensus problem for partitions," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 281-297, September.
    3. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    4. John Geanakoplos, 2005. "Three brief proofs of Arrow’s Impossibility Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 211-215, July.
    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.
    7. Jean-Pierre Barthélemy & Bruno Leclerc & Bernard Monjardet, 1986. "On the use of ordered sets in problems of comparison and consensus of classifications," Journal of Classification, Springer;The Classification Society, vol. 3(2), pages 187-224, September.
    8. Dimitrov, Dinko & Sung, Shao Chin & Xu, Yongsheng, 2007. "Procedural group identification," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 137-146, September.
    9. Miller, Alan D., 2008. "Group identification," Games and Economic Behavior, Elsevier, vol. 63(1), pages 188-202, May.
    10. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
    11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    12. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 61-65, March.
    13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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    Cited by:

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    3. Carlos Hervés-Beloso & Claudia Meo & Emma Moreno-García, 2014. "Information and size of coalitions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 545-563, April.
    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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