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The McGarvey problem in judgement aggregation

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  • Pivato, Marcus
  • Nehring, Klaus

Abstract

`Judgement aggregation' is a model of social choice where the space of social alternatives is the set of consistent truth-valuations (`judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. We show that, for a variety of spaces, propositionwise majority voting can yield any possible judgement. By considering the geometry of sub-polytopes of the Hamming cube, we also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of McGarvey (1953) and Stearns (1959).

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22600.

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Date of creation: 10 May 2010
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Handle: RePEc:pra:mprapa:22600

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Keywords: judgement aggregation; majority vote; McGarvey; Stearns; 0/1 polytope; Hamming cube;

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References

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  1. 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.
  2. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
  3. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
  4. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
  5. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
  6. Elad Dokow & Ron Holzman, 2009. "Aggregation of binary evaluations for truth-functional agendas," Social Choice and Welfare, Springer, vol. 32(2), pages 221-241, February.
  7. 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.
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Cited by:
  1. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2011. "Condorcet admissibility: Indeterminacy and path-dependence under majority voting on interconnected decisions," MPRA Paper 32434, University Library of Munich, Germany.
  2. Nehring, Klaus & Pivato, Marcus, 2013. "Majority rule in the absence of a majority," MPRA Paper 46721, University Library of Munich, Germany.
  3. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2013. "The Condorcet set: Majority voting over interconnected propositions," Working Paper Series in Economics 51, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.

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