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On the impossibility of preference aggregation under uncertainty

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Abstract

We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are smooth. The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences

Suggested Citation

  • Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2005. "On the impossibility of preference aggregation under uncertainty," Cahiers de la Maison des Sciences Economiques v05012, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:v05012
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    1. Paolo Ghirardato & Massimo Marinacci, 2001. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 864-890, November.
    2. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, vol. 47(2), pages 177-183, February.
    3. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    4. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. Charles Blackorby & David Donaldson & Philippe Mongin, 2004. "Social Aggregation Without the Expected Utility Hypothesis," Working Papers hal-00242932, HAL.
    7. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    8. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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    Cited by:

    1. Marcello Basili, 2008. "The global strategy to cope with H5N1: the property rights caveat," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 0908, Department of Economic Policy, Finance and Development (DEPFID), University of Siena.
    2. Antoine Bommier & Stéphane Zuber, 2012. "The Pareto Principle Of Optimal Inequality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(2), pages 593-608, May.
    3. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.

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    More about this item

    Keywords

    Aggregation; Harsanyi; uncertainty; multiple priors;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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