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On linear aggregation of infinitely many finitely additive probability measures

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  • Michael Nielsen

    (Columbia University)

Abstract

We discuss Herzberg’s (Theory Decis 78(2):319–337, 2015) treatment of linear aggregation for profiles of infinitely many finitely additive probabilities and suggest a natural alternative to his definition of linear continuous aggregation functions. We then prove generalizations of well-known characterization results due to (J Am Stat Assoc 76(374):410–414, 1981). We also characterize linear aggregation of probabilities in terms of a Pareto condition, de Finetti’s notion of coherence, and convexity.

Suggested Citation

  • Michael Nielsen, 2019. "On linear aggregation of infinitely many finitely additive probability measures," Theory and Decision, Springer, vol. 86(3), pages 421-436, May.
    • Handle: RePEc:kap:theord:v:86:y:2019:i:3:d:10.1007_s11238-019-09690-y
    DOI: 10.1007/s11238-019-09690-y
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    References listed on IDEAS

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    1. Diecidue, Enrico & Wakker, Peter P., 2002. "Dutch books: avoiding strategic and dynamic complications, and a comonotonic extension," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 135-149, March.
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    4. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    5. Enrico Diecidue, 2006. "Deriving Harsanyi’s Utilitarianism from De Finetti’s Book-Making Argument," Theory and Decision, Springer, vol. 61(4), pages 363-371, December.
    6. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2014. "A unifying view on some problems in probability and statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 483-500, November.
    7. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, vol. 78(2), pages 319-337, February.
    8. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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    Cited by:

    1. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    2. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.
    3. Minkyung Wang, 2024. "Aggregating individual credences into collective binary beliefs: an impossibility result," Theory and Decision, Springer, vol. 97(1), pages 39-66, August.

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