Economic Theory

, Volume 51, Issue 1, pp 191–212 | Cite as

Separability and aggregation of equivalence relations

  • Dinko Dimitrov
  • Thierry Marchant
  • Debasis MishraEmail author
Research Article


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.


Aggregation Equivalence relations Separability Unanimity Pareto axiom 

JEL Classification

C0 D0 


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  1. Ahn, D.S., Chambers C.P.: What’s on the menu? Deciding what is available to the group? Working paper. University of California, Berkeley (2010)Google Scholar
  2. Arrow K.J.: Social Choice and Individual Values. pp. 1963, 2nd edn. Wiley, New York (1951)Google Scholar
  3. Barthélemy J.P., Leclerc B., Monjardet B.: On the use of ordered sets in problems of comparison and consensus of classifications. J Classif 3, 187–224 (1986)CrossRefGoogle Scholar
  4. Barthélemy J.P.: Comments on: aggregation of equivalence relations by P.C. Fishburn and A. Rubinstein. J Classifs 5, 85–87 (1988)CrossRefGoogle Scholar
  5. Çengelci M., Sanver R.: Simple collective identity functions. Theory Decis 68, 417–443 (2010)CrossRefGoogle Scholar
  6. Chambers C.P., Miller A.: Rules for information aggregation. Soc Choice Welf 36, 75–82 (2011)CrossRefGoogle Scholar
  7. Dimitrov D., Puppe C.: Note on non-bossy social classification, working paper. Karlsruhe Institute of Technology, Karlsruhe (2010)Google Scholar
  8. Dimitrov D., Sung S.-C., Xu Y.: Procedural group identification. Math Soc Sci 54, 137–146 (2007)CrossRefGoogle Scholar
  9. Fishburn P.C., Rubinstein A.: Aggregation of equivalence relations. J Classif 3, 61–65 (1986)CrossRefGoogle Scholar
  10. Geanakoplos J.: Three brief proofs of arrow’s impossibility theorem. Econ Theory 26, 211–215 (2005)CrossRefGoogle Scholar
  11. Hart S., Mas-Colell A.: Potential, value and consistency. Econometrica 57, 589–614 (1989)CrossRefGoogle Scholar
  12. Houy N.: “I want to be a J!” : Liberalism in group identification problems. Math Soc Sci 54, 59–70 (2007)CrossRefGoogle Scholar
  13. Kasher A., Rubinstein A.: On the question “Who is a J?” a social choice approach. Logique et Analyse 160, 385–395 (1997)Google Scholar
  14. Leclerc B.: Efficient and binary consensus functions on transitively valued relations. Math Soc Sci 8, 45–61 (1984)CrossRefGoogle Scholar
  15. Miller A.: Group identification. Games Econ Behav 63, 188–202 (2008)CrossRefGoogle Scholar
  16. Mirkin B.: On the problem of reconciling partitions. In: Blalock, H.M., Aganbegian, A., Borodkin, F., Boudon, R., Capecchi, V. (eds) Quantitative sociology, International Perspectives on Mathematical and Statistical Modelling, pp. 441–449. Academic Press, New York (1975)Google Scholar
  17. Neumann D.A., Norton V.T. Jr.: Clustering and isolation in the consensus problem. J Classif 3, 281–297 (1986)CrossRefGoogle Scholar
  18. Perote-Pena J., Piggins A.: Geometry and impossibility. Econ Theory 20, 831–836 (2002)CrossRefGoogle Scholar
  19. Rubinstein A., Fishburn P.C.: Algebraic aggregation theory. J Econ Theory 38, 63–77 (1986)CrossRefGoogle Scholar
  20. Samet D., Schmeidler D.: Between liberalism and democracy. J Econ Theory 110, 213–233 (2003)CrossRefGoogle Scholar
  21. Shapley L.: Contributions to the theory of game II (Annals of mathematics studies 28). In: Kuhn, H.W., Tucker, A.W. (eds) chapter A Value for n-Person Games, pp. 307–317. Princeton University Press, Princeton (1953)Google Scholar
  22. Ubeda L.: Neutrality in Arrow and other impossibility theorems. Econ Theory 23, 195–204 (2004)CrossRefGoogle Scholar
  23. Wilson R.: On the theory of aggregation. J Econ Theory 10, 89–99 (1978)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Dinko Dimitrov
    • 1
  • Thierry Marchant
    • 2
  • Debasis Mishra
    • 3
    Email author
  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.Ghent UniversityGhentBelgium
  3. 3.Indian Statistical InstituteNew DelhiIndia

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