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The impossibility of non-manipulable probability aggregation

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  • Franz Dietrich

    (CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Christian List

    (LMU - Fakultät für Physik - Ludwig-Maximilians-Universität [München/Munich] - LMU - Ludwig-Maximilians University [Munich])

Abstract

A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is "non-manipulable" if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function ("strategic voting"). We show that, except in trivial cases, no probability aggregation rule satisfying two mild conditions (non-dictatorship and consensus preservation) is non-manipulable.

Suggested Citation

  • Franz Dietrich & Christian List, 2024. "The impossibility of non-manipulable probability aggregation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-04405495, HAL.
    • Handle: RePEc:hal:cesptp:halshs-04405495
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04405495
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    References listed on IDEAS

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    1. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    2. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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