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Representation and aggregation of preferences under uncertainty

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  • Gajdos, T.
  • Tallon, J.-M.
  • Vergnaud, J.-C.

Abstract

We axiomatize in the Anscombe-Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.

Suggested Citation

  • Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, vol. 141(1), pages 68-99, July.
  • Handle: RePEc:eee:jetheo:v:141:y:2008:i:1:p:68-99
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    Cited by:

    1. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    2. Nascimento, Leandro, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    3. repec:hal:cesptp:hal-01241819 is not listed on IDEAS
    4. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    5. Hill, Brian, 2012. "Unanimity and the aggregation of multiple prior opinions," HEC Research Papers Series 959, HEC Paris.
    6. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    7. Sara Amoroso & Pietro Moncada-Paternò-Castello & Antonio Vezzani, 2017. "R&D profitability: the role of risk and Knightian uncertainty," Small Business Economics, Springer, vol. 48(2), pages 331-343, February.
    8. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    9. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    10. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    11. repec:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0004-6 is not listed on IDEAS
    12. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    13. Mongin, Philippe & Pivato, Marcus, 2016. "Social preference under twofold uncertainty," MPRA Paper 71776, University Library of Munich, Germany.
    14. Chew, Soo Hong & Sagi, Jacob S., 2012. "An inequality measure for stochastic allocations," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1517-1544.
    15. Anirudha Balasubramanian, 2015. "On weighted utilitarianism and an application," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(4), pages 745-763, April.
    16. Herzberg, Frederik, 2014. "Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results," Center for Mathematical Economics Working Papers 488, Center for Mathematical Economics, Bielefeld University.
    17. Herzberg, Frederik, 2013. "Arrovian aggregation of MBA preferences: An impossibility result," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79957, Verein für Socialpolitik / German Economic Association.
    18. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 427-452, July.
    19. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS

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