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Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary

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  • Duddy, Conal
  • Piggins, Ashley

Abstract

A model of judgment aggregation is presented in which judgments on propositions are not binary but come in degrees. The primitives are a set of propositions, an entailment relation, and a “triangular norm” which establishes a lower bound on the degree to which a proposition is true whenever it is entailed by a set of propositions. Under standard assumptions, we identify a necessary and sufficient condition for the collective judgments to be both deductively closed and free from veto power. This condition says that the triangular norm used to establish the lower bound must contain a zero divisor.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 148 (2013)
Issue (Month): 2 ()
Pages: 793-805

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Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:793-805

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Judgment aggregation; Deductive closure; Many-valued logic; Triangular norm; Zero divisor;

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References

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  1. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  2. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  3. 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.
  4. Dietrich, Franz & List, Christian, 2006. "Judgment aggregation without full rationality," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  6. Franz Dietrich & Christian List, 2005. "Arrow’s theorem in judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 13, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  7. Conal Duddy & Juan Perote-Peña & Ashley Piggins, 2011. "Arrow’s theorem and max-star transitivity," Social Choice and Welfare, Springer, vol. 36(1), pages 25-34, January.
  8. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
  9. Mongin, Philippe, 2006. "Factoring out the impossibility of logical aggregation," Les Cahiers de Recherche 854, HEC Paris.
  10. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  11. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Cowles Foundation Discussion Papers 1753, Cowles Foundation for Research in Economics, Yale University.
  12. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  13. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
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Cited by:
  1. Dietrich, Franz, 2013. "Judgment aggregation and agenda manipulation," MPRA Paper 51775, University Library of Munich, Germany.
  2. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
  3. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
  4. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.

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