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Judgment aggregation by quota rules

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Author Info

  • Franz Dietrich

    (University of Konstanz, Germany)

  • Christian List

    (London School of Economics, United Kingdom)

Abstract

It is known that majority voting among several individuals on logically interconnected propositions may generate irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds some (proposition-specific) threshold. After characterizing quota rules, we prove necessary and sufficient conditions under which their outcomes satisfy various rationality conditions. We also consider sequential quota rules, which adjudicate propositions sequentially, letting earlier judgments constrain later ones. While ensuring rationality, sequential rules may be path-dependent. We characterize path-independence and prove its equivalence to strategy- proofness under mild conditions. Our results generalize earlier (im)possibility theorems.

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File URL: http://128.118.178.162/eps/pe/papers/0501/0501005.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Public Economics with number 0501005.

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Length: 22 pages
Date of creation: 18 Jan 2005
Date of revision:
Handle: RePEc:wpa:wuwppe:0501005

Note: Type of Document - pdf; pages: 22
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Web page: http://128.118.178.162

Related research

Keywords: Judgment aggregation; quota rules; collective rationality; path-dependence; strategy-proofness; formal logic;

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References

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  1. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  2. 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.
  3. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
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Citations

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Cited by:
  1. 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).
  2. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
  3. Dietrich, Franz & List, Christian, 2007. "The impossibility of unbiased judgment aggregation," Research Memorandum 022, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  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. Dietrich, Franz, 2010. "The possibility of judgment aggregation on agendas with subjunctive implications," Journal of Economic Theory, Elsevier, vol. 145(2), pages 603-638, March.
  6. Christian List & Ben Polak, 2010. "Introduction to Judgment Aggregation," Cowles Foundation Discussion Papers 1753, Cowles Foundation for Research in Economics, Yale University.
  7. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.
  8. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  9. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
  10. Mongin, Philippe, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," MPRA Paper 37752, University Library of Munich, Germany.
  11. 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).

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