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Harsanyi's aggregation theorem with incomplete preferences

Author

Listed:
  • Eric Danan

    () (THEMA, Universite de Cergy-Pontoise and THEMA)

  • Thibault Gajdos

    () (GREQAM, CNRS, Aix-Marseille University)

  • Jean-Marc Tallon

    () (Universite Paris I Pantheon-Sorbonne, CNRS)

Abstract

We provide a generalization of Harsanyi (1955)'s aggregation theorem to the case of incomplete preferences at the individual and social level. Individuals and society have possibly incomplete expected utility preferences that are represented by sets of expected utility functions. Under Pareto indifference, social preferences are represented through a set of aggregation rules that are utilitarian in a generalized sense. Strengthening Pareto indifference to Pareto preference provides a refinement of the representation.

Suggested Citation

  • Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2013. "Harsanyi's aggregation theorem with incomplete preferences," THEMA Working Papers 2013-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2013-05
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    References listed on IDEAS

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    1. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2010. "Aggregating sets of von Neumann-Morgenstern," Documents de travail du Centre d'Economie de la Sorbonne 10068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Mongin, P & d'Aspremont, C, 1996. "Utility Theory and Ethics," Papers 9632, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    3. Chambers, Christopher P. & Hayashi, Takashi, 2006. "Preference aggregation under uncertainty: Savage vs. Pareto," Games and Economic Behavior, Elsevier, vol. 54(2), pages 430-440, February.
    4. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    5. De Meyer, Bernard & Mongin, Philippe, 1995. "A note on affine aggregation," Economics Letters, Elsevier, pages 177-183.
    6. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    7. Gajdos, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Representation and aggregation of preferences under uncertainty," Journal of Economic Theory, Elsevier, pages 68-99.
    8. Juan Dubra & Efe A. Ok, 2002. "A Model of Procedural Decision Making in the Presence of Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1053-1080, November.
    9. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, pages 118-133.
    10. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    11. Danan, Eric & Gajdos, Thibault & Tallon, Jean-Marc, 2013. "Aggregating sets of von Neumann–Morgenstern utilities," Journal of Economic Theory, Elsevier, pages 663-688.
    12. Lloyd S. Shapley & Manel Baucells, 1998. "Multiperson Utility," UCLA Economics Working Papers 779, UCLA Department of Economics.
    13. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    14. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
    15. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-1336, November.
    16. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 575-592.
    17. Zhou, Lin, 1997. "Harsanyi's Utilitarianism Theorems: General Societies," Journal of Economic Theory, Elsevier, vol. 72(1), pages 198-207, January.
    18. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 123-139, January.
    19. repec:hal:cesptp:halshs-00788647 is not listed on IDEAS
    20. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
    21. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309-309.
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    1. repec:hal:cesptp:hal-01241819 is not listed on IDEAS
    2. Gérard Mondello, 2015. "Civil liability, Knight's UnCertainty and non-diCtatorial regUlator Documents de travail GREDEG GREDEG Working Papers Series," Working Papers hal-01251437, HAL.

    More about this item

    Keywords

    Incomplete preferences; aggregation; expected multi-utility; utilitarianism.;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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