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

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

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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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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  1. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  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. 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.
  4. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer, vol. 33(4), pages 559-574, November.
  5. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
  6. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
  7. Christian List, 2002. "A Model of Path-Dependence in Decisions over Multiple Propositions," Economics Papers 2002-W15, Economics Group, Nuffield College, University of Oxford.
  8. 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.
  9. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.
  10. 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.
  11. Miller, Alan D., 2013. "Community standards," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2696-2705.
  12. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  13. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
  14. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
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