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Majority rule in the absence of a majority

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  • Nehring, Klaus
  • Pivato, Marcus

Abstract

What is the meaning of "majoritarianism" as a principle of democratic group decision-making in a judgement aggregation problem, when the propositionwise majority view is logically inconsistent? We argue that the majoritarian ideal is best embodied by the principle of "supermajority efficiency" (SME). SME reflects the idea that smaller supermajorities must yield to larger supermajorities. We show that in a well-demarcated class of judgement spaces, the SME outcome is generically unique. But in most spaces, it is not unique; we must make trade-offs between the different supermajorities. We axiomatically characterize the class of "additive majority rules", which specify how such trade-offs are made. This requires, in general, a hyperreal-valued representation.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 46721.

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Date of creation: 02 May 2013
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Handle: RePEc:pra:mprapa:46721

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Keywords: judgement aggregation; majority rule; majoritarian; hyperreal; Condorcet;

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  1. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 89-110, April.
  2. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer, Springer, vol. 33(4), pages 559-574, November.
  3. 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.
  4. 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.
  5. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 512-543, March.
  6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(1), pages 89-99, February.
  7. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, Elsevier, vol. 12(3), pages 472-482, June.
  8. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.
  9. 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.
  10. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(2), pages 583-602, March.
  11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(1), pages 63-77, February.
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