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Judgment aggregation without full rationality

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  • Dietrich, Franz
  • List, Christian

    (METEOR)

Abstract

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinstein''s group identification problem.

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Bibliographic Info

Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 023.

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Date of creation: 2007
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Handle: RePEc:dgr:umamet:2007023

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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm

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Keywords: mathematical economics;

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References

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  1. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  2. Philippe Mongin, 2005. "Factoring Out the Impossibility of Logical Aggregation," Working Papers hal-00243010, HAL.
  3. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
  4. Franz Dietrich & Christian List, 2004. "Strategy-proof judgment aggregation," Public Economics 0404007, EconWPA, revised 25 Jul 2005.
  5. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
  6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  7. Dietrich, Franz & List, Christian, 2007. "Arrow's theorem in judgment aggregation," Open Access publications from Maastricht University urn:nbn:nl:ui:27-15414, Maastricht University.
  8. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics 0501005, EconWPA.
  9. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
  10. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Open Access publications from Maastricht University urn:nbn:nl:ui:27-15418, Maastricht University.
  11. Dietrich, Franz, 2007. "A generalised model of judgment aggregation," Open Access publications from Maastricht University urn:nbn:nl:ui:27-15416, Maastricht University.
  12. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  13. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
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Citations

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Cited by:
  1. Dietrich, Franz & List, Christian, 2007. "The impossibility of unbiased judgment aggregation," Research Memoranda 022, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
  2. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Cowles Foundation Discussion Papers 1753, Cowles Foundation for Research in Economics, Yale University.
  3. Jean-François Bonnefon, 2010. "Behavioral evidence for framing effects in the resolution of the doctrinal paradox," Social Choice and Welfare, Springer, vol. 34(4), pages 631-641, April.
  4. García-Bermejo, Juan Carlos, 2012. "A Pooling Approach to Judgment Aggregation," Working Papers in Economic Theory 2012/01, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  5. García-Bermejo, Juan Carlos, 2013. "A Non-Proposition-Wise Variant of Majority Voting for Aggregating Judgments," Working Papers in Economic Theory 2013/02, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  6. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  7. Herzberg, Frederik, 2010. "Judgment aggregators and Boolean algebra homomorphisms," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 132-140, January.
  8. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  9. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  10. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer, vol. 32(4), pages 575-601, May.

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