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The Condorcet set: Majority voting over interconnected propositions

  • Nehring, Klaus
  • Pivato, Marcus
  • Puppe, Clemens

Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations (views) on a family of logically interconnected propositions, or yes/no-issues. Yet, simply complying with the majority opinion in each issue often yields a logically inconsistent collection of judgements. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority on a maximal set of issues. The elements of this set are exactly those that can be obtained through sequential majority voting, according to which issues are sequentially decided by simple majority unless earlier choices logically force the opposite decision. We investigate the size and structure of the Condorcet set - and hence the properties of sequential majority voting - for several important classes of judgement aggregation problems. While the Condorcet set verifies McKelvey's (1979) celebrated chaos theorem in a number of contexts, in others it is shown to be very regular and well-behaved.

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Paper provided by Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering in its series Working Paper Series in Economics with number 51.

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Date of creation: 2013
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Handle: RePEc:zbw:kitwps:51
Contact details of provider: Web page: http://www.wiwi.kit.edu/

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  1. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.
  2. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
  3. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer, vol. 33(4), pages 559-574, November.
  4. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
  5. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
  6. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2696-2705.
  7. Peter Fishburn & Ariel Rubinstein, 1986. "Aggregation of equivalence relations," Journal of Classification, Springer, vol. 3(1), pages 61-65, March.
  8. 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.
  9. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer, vol. 28(3), pages 491-506, April.
  10. Dinko Dimitrov & Thierry Marchant & Debasis Mishra, 2009. "Separability and aggregation of equivalence relations," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 09-06, Indian Statistical Institute, New Delhi, India.
  11. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2013. "Unanimity overruled: Majority voting and the burden of history," Working Paper Series in Economics 50, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  12. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
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