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Aggregating sets of von Neumann–Morgenstern utilities

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  • Danan, Eric
  • Gajdos, Thibault
  • Tallon, Jean-Marc

Abstract

We analyze the preference aggregation problem without the assumption that individuals and society have fully determined and observable preferences. More precisely, we endow individuals and society with sets of possible von Neumann–Morgenstern utility functions over lotteries. We generalize the classical Pareto and Independence of Irrelevant Alternatives axioms and show they imply a generalization of the classical neutrality assumption. We then characterize the class of neutral social welfare functions. This class is considerably broader for indeterminate than for determinate utilities, where it basically reduces to utilitarianism. We finally characterize several classes of neutral social welfare functions for indeterminate utilities, including the utilitarian and “multi-utilitarian” classes.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 148 (2013)
Issue (Month): 2 ()
Pages: 663-688

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Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:663-688

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

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. 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.
  3. Philippe Mongin, 2001. "A note on mixture sets in decision theory," Decisions in Economics and Finance, Springer, vol. 24(1), pages 59-69, 05.
  4. 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).
  5. 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.
  6. 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.
  7. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
  8. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-72, October.
  9. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
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Cited by:
  1. Eric Danan & Thilbault Gajdos & Jean-Marc Tallon, 2012. "Harsanyi's aggregation theorem with incomplete preferences," Documents de travail du Centre d'Economie de la Sorbonne 12082, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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