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Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions

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

Abstract

Judgement aggregation is a model of social choice where the space of social alternatives is the set of consistent evaluations (`views') on a family of logically interconnected propositions, or yes/no-issues. Unfortunately, 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 in as many issues as possible. Any element of this set can be obtained through a process of diachronic judgement aggregation, where the evaluations of the individual issues are decided through a sequence of majority votes unfolding over time, with earlier decisions possibly imposing logical constraints on later decisions. Thus, for a fixed profile of votes, the ultimate social choice can depend on the order in which the issues are decided; this is called path dependence. We investigate the size and structure of the Condorcet set ---and hence the scope and severity of path-dependence ---for several important classes of judgement aggregation problems.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32434.

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Date of creation: 24 Jul 2011
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Handle: RePEc:pra:mprapa:32434

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Keywords: judgement aggregation; diachronic; path-dependence; indeterminacy; Condorcet; median rule; majoritarian;

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  1. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 544-561, March.
  2. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1085-1112, September.
  3. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 495-511, March.
  4. 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.
  5. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(6), pages 2696-2705.
  6. John Duggan, 2007. "A systematic approach to the construction of non-empty choice sets," Social Choice and Welfare, Springer, Springer, vol. 28(3), pages 491-506, April.
  7. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, Elsevier, vol. 1(3), pages 235-267, May.
  8. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Series Working Papers 2002-W15, University of Oxford, Department of Economics.
  9. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 512-543, March.
  10. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer, Springer, vol. 33(4), pages 559-574, November.
  11. 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, Elsevier, vol. 135(1), pages 269-305, July.
  12. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  13. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 467-494, March.
  14. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.
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Cited by:
  1. Nehring, Klaus & Pivato, Marcus, 2013. "Majority rule in the absence of a majority," MPRA Paper 46721, University Library of Munich, Germany.
  2. Dietrich, Franz, 2011. "Scoring rules for judgment aggregation," MPRA Paper 35657, University Library of Munich, Germany.
  3. 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).
  4. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, Springer, vol. 40(2), pages 581-630, February.

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