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Strategy-proof judgment aggregation

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  • Franz Dietrich
  • Christian List
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    Abstract

    Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

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    File URL: http://eprints.lse.ac.uk/5812/
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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 5812.

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    Date of creation: 2007
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    Publication status: Published in Economics and Philosophy, 2007, 23(3), pp. 269-300. ISSN: 1474-0028
    Handle: RePEc:ehl:lserod:5812

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    References

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    1. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    2. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer, vol. 29(1), pages 19-33, July.
    3. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    4. Franz Dietrich, 2005. "Judgment aggregation in general logics," Public Economics 0505007, EconWPA.
    5. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
    6. Christian List, 2005. "The probability of inconsistencies in complex collective decisions," Social Choice and Welfare, Springer, vol. 24(1), pages 3-32, 05.
    7. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    8. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    9. 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.
    10. Brennan, Geoffrey, 2001. "Collective coherence?," International Review of Law and Economics, Elsevier, vol. 21(2), pages 197-211, June.
    11. Baigent, Nick, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, MIT Press, vol. 102(1), pages 161-69, February.
    12. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    13. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
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    Cited by:
    1. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
    2. Christian List, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.
    3. Franz Dietrich & Philippe Mongin, 2010. "The premiss-based approach to judgment aggregation," LSE Research Online Documents on Economics 27896, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. Dietrich, Franz & List, Christian, 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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