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Separability and aggregation of equivalence relations

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Author Info

  • 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

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Bibliographic Info

Paper provided by Indian Statistical Institute, New Delhi, India in its series Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers with number 09-06.

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Length: 23 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:ind:isipdp:09-06

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  1. 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, vol. 3(2), pages 187-224, September.
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  8. Dimitrov, Dinko & Puppe, Clemens, 2011. "Non-bossy social classification," Working Paper Series in Economics 23, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  9. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer, vol. 3(1), pages 61-65, March.
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Cited by:
  1. Christopher Chambers & Alan Miller, 2011. "Rules for aggregating information," Social Choice and Welfare, Springer, vol. 36(1), pages 75-82, January.
  2. repec:hal:journl:halshs-00659190 is not listed on IDEAS
  3. Bruno Leclerc & Bernard Monjardet, 2011. "Aggregation and residuation," Documents de travail du Centre d'Economie de la Sorbonne 11085, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. Carlos Hervés-Beloso & Claudia Meo & Emma Moreno-García, 2014. "Information and size of coalitions," Economic Theory, Springer, vol. 55(3), pages 545-563, April.
  5. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2696-2705.
  6. Chambers, Christopher P. & Miller, Alan D., . "Inefficiency," Working Papers WP2011/14, University of Haifa, Department of Economics, revised 30 Nov 2011.
  7. Mishra, Debasis & Roy, Souvik, 2012. "Strategy-proof partitioning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 285-300.
  8. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2013. "The Condorcet set: Majority voting over interconnected propositions," Working Paper Series in Economics 51, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.

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