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Majority voting on restricted domains

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  • Franz Dietrich
  • Christian List
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    Abstract

    In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments sufficient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen's triplewise value-restriction, itself the most general classic condition. We also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results support the robustness of majority rule.

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    File URL: http://eprints.lse.ac.uk/27902/
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    Bibliographic Info

    Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 27902.

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    Date of creation: Mar 2010
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    Publication status: Published in Journal of Economic Theory, March, 2010, 145(2), pp. 512-543. ISSN: 1095-7235
    Handle: RePEc:ehl:lserod:27902

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    Postal: LSE Library Portugal Street London, WC2A 2HD, U.K.
    Phone: +44 (020) 7405 7686
    Web page: http://www.lse.ac.uk/
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    Related research

    Keywords: Judgment aggregation; Domain restriction; Majority voting; Consistency; Value-restriction; Analogues of single-peakedness; May's theorem;

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    References

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    1. Franz Dietrich & Christian List, 2005. "Arrow’s theorem in judgment aggregation," STICERD - Political Economy and Public Policy Paper Series 13, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
    3. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer, vol. 31(1), pages 41-57, June.
    4. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer, vol. 28(4), pages 529-565, June.
    5. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, October.
    6. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer, vol. 31(1), pages 15-39, June.
    7. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy.
    8. Franz Dietrich & Christian List, 2007. "Strategy-proof judgment aggregation," LSE Research Online Documents on Economics 5812, London School of Economics and Political Science, LSE Library.
    9. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
    10. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
    11. Martin Hees, 2007. "The limits of epistemic democracy," Social Choice and Welfare, Springer, vol. 28(4), pages 649-666, June.
    12. Franz Dietrich & Christian List, 2004. "Strategy-proof judgment aggregation," Public Economics 0404007, EconWPA, revised 25 Jul 2005.
    13. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    14. Alejandro Saporiti & Fernando Tohmé, 2003. "Single-Crossing, Strategic Voting and the Median Choice Rule," CEMA Working Papers: Serie Documentos de Trabajo. 237, Universidad del CEMA.
    15. 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. Christian List & Ben Polak, 2010. "Introduction to judgment aggregation," LSE Research Online Documents on Economics 27900, London School of Economics and Political Science, LSE Library.
    2. 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).
    3. repec:spo:wpecon:info:hdl:2441/dambferfb7dfprc9m2e02cub3 is not listed on IDEAS

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