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

  • Duddy, Conal
  • Piggins, Ashley

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Franz Dietrich & Christian List, 2005. "Arrow’s theorem in judgment aggregation," LSE Research Online Documents on Economics 19295, London School of Economics and Political Science, LSE Library.
  2. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  3. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
  4. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Cowles Foundation Discussion Papers 1753, Cowles Foundation for Research in Economics, Yale University.
  5. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
  6. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  7. 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).
  8. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  9. 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.
  10. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
  11. 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.
  12. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  13. Richard Barrett & Maurice Salles, 2006. "Social Choice With Fuzzy Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200615, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  14. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
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