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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 independent (i.e., propositionwise) aggregation rules 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 (strong) 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 University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 032.

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Date of creation: 2006
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Handle: RePEc:unm:umamet:2006032

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Keywords: mathematical economics;

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References

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  1. 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.
  2. Dov Samet & David Schmeidler, 1999. "Between Liberalism and Democracy," Game Theory and Information, EconWPA 9908001, EconWPA.
  3. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, Elsevier, vol. 80(3), pages 379-382, September.
  4. Franz Dietrich & Christian List, 2005. "Arrow's Theorem in Judgement Aggregation," Public Economics, EconWPA 0504007, EconWPA, revised 10 Sep 2005.
  5. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics, EconWPA 0505007, EconWPA.
  6. Mongin, Philippe, 2006. "Factoring out the impossibility of logical aggregation," Les Cahiers de Recherche 854, HEC Paris.
  7. Franz Dietrich & Christian List, 2005. "Judgment aggregation by quota rules," Public Economics, EconWPA 0501005, EconWPA.
  8. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(1), pages 63-77, February.
  9. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(1), pages 89-99, February.
  10. Franz Dietrich & Christian List, 2005. "Strategy-proof judgment aggregation," STICERD - Political Economy and Public Policy Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, Elsevier, vol. 126(1), pages 286-298, January.
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