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Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results

Author

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  • Herzberg, Frederik

    (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.

Suggested Citation

  • Herzberg, Frederik, 2014. "Aggregation of Monotonic Bernoullian Archimedean preferences: Arrovian impossibility results," Center for Mathematical Economics Working Papers 488, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:488
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    File URL: https://pub.uni-bielefeld.de/download/2675233/2901857
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
    6. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    7. Herzberg, Frederik & Eckert, Daniel, 2017. "Impossibility results for infinite-electorate abstract aggregation rules," Center for Mathematical Economics Working Papers 427, Center for Mathematical Economics, Bielefeld University.
    8. 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.
    9. Lauwers, Luc & Van Liedekerke, Luc, 1995. "Ultraproducts and aggregation," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 217-237.
    10. Campbell, Donald E., 1990. "Intergenerational social choice without the Pareto principle," Journal of Economic Theory, Elsevier, vol. 50(2), pages 414-423, April.
    11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    12. 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.
    13. 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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    Citations

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    Cited by:

    1. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    2. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    3. repec:hal:cesptp:hal-01241819 is not listed on IDEAS
    4. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2014. "Aggregating Tastes, Beliefs, and Attitudes under Uncertainty," Documents de travail du Centre d'Economie de la Sorbonne 14063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, pages 319-337.

    More about this item

    Keywords

    impossibility result; Arrow’s theorem; ultrafilter; Arrovian social choice; Knightian uncertainty; expectedutility; ambiguity; Monotonic Bernoullian Archimedean (MBA) preferences; ultraproduct;

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