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Social Choice and Welfare

, Volume 36, Issue 1, pp 75–82 | Cite as

Rules for aggregating information

  • Christopher P. Chambers
  • Alan D. Miller
Original Paper

Abstract

We present a model of information aggregation in which agents’ information is represented through partitions over states of the world. We discuss three axioms, meet separability, upper unanimity, and non-imposition, and show that these three axioms characterize the class of oligarchic rules, which combine all of the information held by a pre-specified set of individuals.

Keywords

Equivalence Relation Group Signal Aggregation Rule Individual Signal Unique Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aigner M (1979) Combinatorial theory. Springer-Verlag, BerlinGoogle Scholar
  2. Barthélemy JP (1988) Comments on “aggregation of equivalence relations” by PC. Fishburn and A. Rubinstein. J Classif 5: 85–87CrossRefGoogle Scholar
  3. Barthélemy J-P, Leclerc B, Monjardet B (1986) On the use of ordered sets in problems of comparison and consensus of classifications. J Classif 3: 187–224CrossRefGoogle Scholar
  4. Birkhoff G (1973) Lattice theory, 3rd edn. American Mathematical Society, Providence, RIGoogle Scholar
  5. Blyth T, Janowitz M (1972) Residuation theory. Pergamon Press, OxfordGoogle Scholar
  6. Davey BA, Priestley HA (2002) Introduction to lattices and order. 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  7. Day WH, McMorris FR (2003) Axiomatic consensus theory in group choice and biomathematics. Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar
  8. Dimitrov D, Marchant T, Mishra D (2009) Separability and aggregation of equivalence relations. Working PaperGoogle Scholar
  9. Fishburn PC, Rubinstein A (1986) Aggregation of equivalence relations. J Classif 3: 61–65CrossRefGoogle Scholar
  10. Grätzer G (2003) General lattice theory, 2nd edn. Birkhäuser Verlag, BaselGoogle Scholar
  11. Holmstrom B, Myerson RB (1983) Efficient and durable decision rules with incomplete information. Econometrica 51: 1799–1819CrossRefGoogle Scholar
  12. Leclerc B (1984) Efficient and binary consensus functions on transitively valued relations. Math Soc Sci 8: 45–61CrossRefGoogle Scholar
  13. Miller AD (2008) Group identification. Games Econ Behav 63: 188–202CrossRefGoogle Scholar
  14. Mirkin BG (1975) On the problem of reconciling partitions. In: Blalock HM (eds) Quantitative sociology: international perspectives on mathematical and statistical modeling, Chap. 15. Academic Press, New York, pp 441–449Google Scholar
  15. Nehring K (2006) Oligarchies in judgment aggregation, Working PaperGoogle Scholar
  16. Ore Ø (1942) Theory of equivalence relations. Duke Math J 9: 573–627CrossRefGoogle Scholar
  17. Roman S (2008) Lattices and ordered sets. Springer, New YorkGoogle Scholar
  18. Szasz G (1964) Introduction to lattice theory. Academic Press, New YorkGoogle Scholar
  19. Vannucci S (2008) The libertarian identification rule in finite atomistic lattices. Working PaperGoogle Scholar
  20. Wilson R (1978) Information, efficiency, and the core of an economy. Econometrica 56: 807–816CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Division of the Humanities and Social Sciences, Mail Code 228-77California Institute of TechnologyPasadenaUSA
  2. 2.Faculty of Law and Department of EconomicsUniversity of Haifa, Mount CarmelHaifaIsrael

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