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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
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    Cited by:

    1. 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.
    2. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, vol. 78(2), pages 319-337, February.
    3. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    4. 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.
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