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Separability and aggregation of equivalence relations

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  • Dinko Dimitrov
  • Thierry Marchant
  • Debasis Mishra

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. Copyright Springer-Verlag 2012

Suggested Citation

  • Dinko Dimitrov & Thierry Marchant & Debasis Mishra, 2012. "Separability and aggregation of equivalence relations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 191-212, September.
    • Handle: RePEc:spr:joecth:v:51:y:2012:i:1:p:191-212
    DOI: 10.1007/s00199-011-0601-2
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    1. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    2. Miller, Alan D., 2008. "Group identification," Games and Economic Behavior, Elsevier, vol. 63(1), pages 188-202, May.
    3. Dimitrov, Dinko & Sung, Shao Chin & Xu, Yongsheng, 2007. "Procedural group identification," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 137-146, September.
    4. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    5. Dimitrov, Dinko & Puppe, Clemens, 2011. "Non-bossy social classification," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 162-165.
    6. 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.
    7. Murat Çengelci & M. Sanver, 2010. "Simple Collective Identity Functions," Theory and Decision, Springer, vol. 68(4), pages 417-443, April.
    8. 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.
    9. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 61-65, March.
    10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    11. 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.
    12. 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.
    13. Leclerc, B., 1984. "Efficient and binary consensus functions on transitively valued relations," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 45-61, August.
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    Cited by:

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    2. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    3. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2696-2705.
    4. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
    5. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    6. 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.
    7. Chambers, Christopher P. & Miller, Alan D., 2018. "Benchmarking," Theoretical Economics, Econometric Society, vol. 13(2), May.
    8. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
    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.

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    More about this item

    Keywords

    Aggregation; Equivalence relations; Separability; Unanimity; Pareto axiom; C0; D0;
    All these keywords.

    JEL classification:

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

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