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Harsanyi's aggregation theorem with incomplete preferences

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  • Eric Danan

    ()
    (THEMA - Théorie économique, modélisation et applications - CNRS : UMR8184 - Université de Cergy Pontoise)

  • Thibault Gajdos

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - École des Hautes Études en Sciences Sociales (EHESS) - CNRS : UMR7316)

  • Jean-Marc Tallon

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00941799.

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Date of creation: Jan 2014
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Handle: RePEc:hal:cesptp:halshs-00941799

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Keywords: Incomplete preferences; aggregation; expected multi-utility; utilitarianism;

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References

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  1. De Meyer, B. & Mongin, P., . "A note on affine aggregation," CORE Discussion Papers RP -1136, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Özgür Evren, 2008. "On the existence of expected multi-utility representations," Economic Theory, Springer, vol. 35(3), pages 575-592, June.
  3. repec:hal:cesptp:halshs-00788647 is not listed on IDEAS
  4. Mongin, P., . "Consistent Bayesian aggregation," CORE Discussion Papers RP -1176, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2013. "Aggregating sets of von Neumann-Morgenstern utilities," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00788647, HAL.
  6. Manel Baucells & Lloyd S. Shapley, 2000. "Multiperson Utility," Econometric Society World Congress 2000 Contributed Papers 0078, Econometric Society.
  7. Mongin, P & d'Aspremont, C, 1996. "Utility Theory and Ethics," Papers 9632, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  8. Zhou, Lin, 1997. "Harsanyi's Utilitarianism Theorems: General Societies," Journal of Economic Theory, Elsevier, vol. 72(1), pages 198-207, January.
  9. Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
  10. 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.
  11. 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, 07.
  12. 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.
  13. 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 1321-36, November.
  14. 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.
  15. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
  16. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
  17. 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.
  18. 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.
  19. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  20. Marcus Pivato, 2013. "Risky social choice with incomplete or noisy interpersonal comparisons of well-being," Social Choice and Welfare, Springer, vol. 40(1), pages 123-139, January.
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