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Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results

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Author Info

  • Frederik Herzberg

    (Center for Mathematical Economics, Bielefeld University)

Abstract

Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341--375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA) preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences -- and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory (in the sense of mathematical logic), is employed.

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File URL: http://www.imw.uni-bielefeld.de/n/upload/paper/cb70ab375662576bd1ac5aaf16b3fca4.pdf
File Function: First version, 2013
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 488.

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Length: 15 pages
Date of creation: Sep 2013
Date of revision:
Handle: RePEc:bie:wpaper:488

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Related research

Keywords: ambiguity; Knightian uncertainty; expected utility; Monotonic Bernoullian Archimedean (MBA) preferences; Arrovian social choice; Arrow's theorem; impossibility result; ultrafilter; ultraproduct;

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References

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  1. 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.
  2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
  3. repec:hal:journl:halshs-00266049 is not listed on IDEAS
  4. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  5. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
  6. 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.
  7. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
  8. Frederik Herzberg & Daniel Eckert, 2010. "Impossibility results for infinite-electorate abstract aggregation rules," Working Papers 427, Bielefeld University, Center for Mathematical Economics.
  9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  10. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
  11. Gilboa, I. & Samet, D. & Schmeidler, D., 2001. "Utilitarian Aggregation of Beliefs and Tastes," Papers 2001-17, Tel Aviv.
  12. 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.
  13. Herzberg, Frederik & Eckert, Daniel, 2012. "The model-theoretic approach to aggregation: Impossibility results for finite and infinite electorates," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 41-47.
  14. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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Cited by:
  1. Frederik Herzberg, 2014. "Aggregating infinitely many probability measures," Working Papers 499, Bielefeld University, Center for Mathematical Economics.

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