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A possibility theorem on aggregation over multiple interconnected propositions

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  • List, Christian

Abstract

Drawing on the so-called `doctrinal paradox`, List and Pettit (2002a) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow`s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up a possibiity result, similar in spirit to Black`s median voter theorem (1948). Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individul sets of judgments into collective ones in accordance with the above mentioned minimal conditions.
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Suggested Citation

  • List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
  • Handle: RePEc:eee:matsoc:v:45:y:2003:i:1:p:1-13
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    References listed on IDEAS

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    1. 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.
    2. Brams, Steven J. & Kilgour, D. Marc & Zwicker, William, 1997. "Voting on Referenda: The Separability Problem and Possible Solutions," Working Papers 97-15, C.V. Starr Center for Applied Economics, New York University.
    3. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
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    Citations

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    Cited by:

    1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society.
    2. Dietrich, Franz & List, Christian, 2007. "Strategy-Proof Judgment Aggregation," Economics and Philosophy, Cambridge University Press, pages 269-300.
    3. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    4. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, pages 113-136.
    5. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    6. Franz Dietrich & Christian List, 2007. "Judgment Aggregation By Quota Rules," Journal of Theoretical Politics, , vol. 19(4), pages 391-424, October.
    7. Philippe Mongin, 2012. "The doctrinal paradox, the discursive dilemma, and logical aggregation theory," Theory and Decision, Springer, vol. 73(3), pages 315-355, September.
    8. Osherson, Daniel & Vardi, Moshe Y., 2006. "Aggregating disparate estimates of chance," Games and Economic Behavior, Elsevier, vol. 56(1), pages 148-173, July.
    9. Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    11. Pivato, Marcus, 2008. "The geometry of consistent majoritarian judgement aggregation," MPRA Paper 9608, University Library of Munich, Germany.
    12. Gilbert Laffond & Jean Lainé, 2008. "The Budget-Voting Paradox," Theory and Decision, Springer, vol. 64(4), pages 447-478, June.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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