IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v86y2019i3d10.1007_s11238-019-09690-y.html
   My bibliography  Save this article

On linear aggregation of infinitely many finitely additive probability measures

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-019-09690-y
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-019-09690-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. Zhou, Lin, 1997. "Harsanyi's Utilitarianism Theorems: General Societies," Journal of Economic Theory, Elsevier, vol. 72(1), pages 198-207, January.
    4. Gianluca Cassese, 2015. "Conglomerability and representations," Working Papers 318, University of Milano-Bicocca, Department of Economics, revised 16 Dec 2015.
    5. 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.
    6. Frederik Herzberg, 2015. "Aggregating infinitely many probability measures," Theory and Decision, Springer, vol. 78(2), pages 319-337, February.
    7. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Feng, Tangren & Ke, Shaowei & McMillan, Andrew, 2022. "Utilitarianism and social discounting with countably many generations," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Youcef Askoura & Antoine Billot, 2018. "A probabilistic aggregation rule for large societies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 251-262, October.
    4. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    5. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    6. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    7. Al-Najjar, Nabil I. & Pomatto, Luciano, 2020. "Aggregate risk and the Pareto principle," Journal of Economic Theory, Elsevier, vol. 189(C).
    8. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Nascimento, Leandro, 2011. "Zhou’s aggregation theorems with multiple welfare weights," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 654-658.
    10. Bleichrodt, Han & Diecidue, Enrico & Quiggin, John, 2004. "Equity weights in the allocation of health care: the rank-dependent QALY model," Journal of Health Economics, Elsevier, vol. 23(1), pages 157-171, January.
    11. Christopher P. Chambers & Federico Echenique & Alan D. Miller, 2023. "Decreasing Impatience," American Economic Journal: Microeconomics, American Economic Association, vol. 15(3), pages 527-551, August.
    12. 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.
    13. Xiaosheng Mu & Luciano Pomatto & Philipp Strack & Omer Tamuz, 2021. "Monotone Additive Statistics," Working Papers 2021-36, Princeton University. Economics Department..
    14. Charles Blackorby & Walter Bossert & David Donaldson, 2007. "Variable-population extensions of social aggregation theorems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 567-589, June.
    15. Mandler, Michael, 2005. "Harsanyi's utilitarianism via linear programming," Economics Letters, Elsevier, vol. 88(1), pages 85-90, July.
    16. Ma, Sinong & Safra, Zvi, 2016. "Fairness and Utilitarianism without Independence," CRETA Online Discussion Paper Series 20, Centre for Research in Economic Theory and its Applications CRETA.
    17. Sinong Ma & Zvi Safra, 2019. "Fairness and utilitarianism without independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 29-52, February.
    18. Hougaard, Jens Leth & Keiding, Hans, 2005. "Rawlsian maximin, Dutch books, and non-additive expected utility," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 239-251, November.
    19. Campi, Luciano & Zabaljauregui, Diego, 2020. "Optimal market making under partial information with general intensities," LSE Research Online Documents on Economics 104612, London School of Economics and Political Science, LSE Library.
    20. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1218-1241, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:86:y:2019:i:3:d:10.1007_s11238-019-09690-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.