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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.

Suggested Citation

  • Nehring, Klaus & Pivato, Marcus, 2013. "Majority rule in the absence of a majority," MPRA Paper 46721, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:46721
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    References listed on IDEAS

    as
    1. Nehring, Klaus & Puppe, Clemens, 2010. "Justifiable group choice," Journal of Economic Theory, Elsevier, vol. 145(2), pages 583-602, March.
    2. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    3. 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.
    4. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    5. 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.
    6. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 559-574, November.
    7. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    8. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
    9. Pivato, Marcus & Nehring, Klaus, 2010. "The McGarvey problem in judgement aggregation," MPRA Paper 22600, University Library of Munich, Germany.
    10. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    11. 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.
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    Citations

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    Cited by:

    1. Burka, Dávid & Puppe, Clemens & Szepesváry, László & Tasnádi, Attila, 2016. "Neural networks would 'vote' according to Borda's Rule," Corvinus Economics Working Papers (CEWP) 2016/13, Corvinus University of Budapest.
    2. Jérôme Lang & Gabriella Pigozzi & Marija Slavkovik & Leendert Torre & Srdjan Vesic, 2017. "A partial taxonomy of judgment aggregation rules and their properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 327-356, February.

    More about this item

    Keywords

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

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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