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Aggregating sets of von Neumann-Morgenstern utilities

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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 analyze the aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals ans society with sets of possible von Neumann-Morgenstern utility functions over lotteries. We generalize the classical neutrality assumption to this setting and characterize the class of neutral social welfare function. This class turns out to be considerably broader for indeterminate than for determinate utilities, where it basically reduces to utilitarianism. In particular, aggregation rules may differ by the relationship between individual and social indeterminacy. We characterize several subclasses of neutral aggregation rules and show that utilitarian rules are those that yield the least indeterminate social utilities, although they still fail to systematically yield a determinate social utility.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00788647.

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Date of creation: Mar 2013
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Publication status: Published, Journal of Economic Theory, 2013, 148, 2, 663-688
Handle: RePEc:hal:cesptp:halshs-00788647

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Keywords: Aggregation ; vNM utility ; indeterminacy ; neutrality ; utilitarianism;

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  1. Blau, Julian H, 1971. "Arrow's Theorem with Weak Independence," Economica, London School of Economics and Political Science, vol. 38(152), pages 413-20, November.
  2. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
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  8. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
  9. Philippe Mongin, 2001. "A note on mixture sets in decision theory," Decisions in Economics and Finance, Springer, vol. 24(1), pages 59-69, 05.
  10. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
  11. d'ASPREMONT, Claude & GEVERS, Louis, . "Equity and the informational basis of collective choice," CORE Discussion Papers RP -350, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Green, Jerry & Hojman, Daniel, 2007. "Choice, Rationality and Welfare Measurement," Working Paper Series rwp07-054, Harvard University, John F. Kennedy School of Government.
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Cited by:
  1. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2012. "Harsanyi's aggregation theorem with incomplete preferences," Post-Print halshs-00768894, HAL.
  2. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2014. "Harsanyi's aggregation theorem with incomplete preferences," Documents de travail du Centre d'Economie de la Sorbonne 14002, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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