IDEAS home Printed from https://ideas.repec.org/p/ema/worpap/2014-15.html
   My bibliography  Save this paper

Ranking Multidimensional Alternatives and Uncertain Prospects

Author

Listed:
  • Marcus Pivato

    (Université de Cergy-Pontoise, THEMA)

  • Philippe Mongin

    (Centre National de la Recherche Scienti que and HEC Paris)

Abstract

We introduce a ranking of multidimensional alternatives, including un- certain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically not of the Cartesian product form). We apply these representation to (1) streams of commodity baskets through time, (2) uncertain social prospects, (3) un- certain individual prospects. Concerning (1), we propose a finite horizon variant of Koopmans's (1960) axiomatization of infinite discounted util- ity sums. The main results concern (2). We push the classic comparison between the ex ante and ex post social welfare criteria one step further by avoiding any expected utility assumptions, and as a consequence ob- tain what appears to be the strongest existing form of Harsanyi's (1955) Aggregation Theorem. Concerning (3), we derive a subjective probability for Anscombe and Aumann's (1963) finite case by merely assuming that there are two epistemically independent sources of uncertainty. characteristics.

Suggested Citation

  • Marcus Pivato & Philippe Mongin, 2014. "Ranking Multidimensional Alternatives and Uncertain Prospects," THEMA Working Papers 2014-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2014-15
    as

    Download full text from publisher

    File URL: http://thema.u-cergy.fr/IMG/documents/2014-15.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fleurbaey, Marc, 2009. "Two variants of Harsanyi's aggregation theorem," Economics Letters, Elsevier, vol. 105(3), pages 300-302, December.
    2. Mongin, Philippe, 1998. "The paradox of the Bayesian experts and state-dependent utility theory," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 331-361, April.
    3. 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.
    4. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    5. P. Mongin & C. d'Aspremont, 1996. "Utility theory and ethics," THEMA Working Papers 96-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Ralph L. Keeney, 1981. "Analysis of Preference Dependencies among Objectives," Operations Research, INFORMS, vol. 29(6), pages 1105-1120, December.
    7. 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.
    8. Chateauneuf, Alain & Wakker, Peter, 1993. "From local to global additive representation," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 523-545.
    9. repec:hal:wpspec:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    10. Keeney,Ralph L. & Raiffa,Howard, 1993. "Decisions with Multiple Objectives," Cambridge Books, Cambridge University Press, number 9780521438834.
    11. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    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. Bernhard von Stengel, 1993. "Closure Properties of Independence Concepts for Continuous Utilities," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 346-389, May.
    14. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    15. Browning, Martin, 1991. "A Simple Nonadditive Preference Structure for Models of Household Behavior over Time," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 607-637, June.
    16. Ross M. Starr, 1973. "Optimal Production and Allocation under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 87(1), pages 81-95.
    17. Blackorby, Charles & Donaldson, David & Weymark, John A., 1999. "Harsanyi's social aggregation theorem for state-contingent alternatives1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 365-387, November.
    18. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    19. Hervé Crès & Itzhak Gilboa & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Post-Print hal-00656618, HAL.
    20. Segal, Uzi, 1992. "Additively separable representations on non-convex sets," Journal of Economic Theory, Elsevier, vol. 56(1), pages 89-99, February.
    21. W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
    22. Ralph Keeney & Robert Nau, 2011. "A theorem for Bayesian group decisions," Journal of Risk and Uncertainty, Springer, vol. 43(1), pages 1-17, August.
    23. Charles Blackorby & David Donaldson & Philippe Mongin, 2004. "Social Aggregation Without the Expected Utility Hypothesis," Working Papers hal-00242932, HAL.
    24. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
    25. 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.
    26. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
    27. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    28. Hammond, Peter J, 1981. "Ex-ante and Ex-post Welfare Optimality under Uncertainty," Economica, London School of Economics and Political Science, vol. 48(191), pages 235-250, August.
    29. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    30. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
    Full references (including those not matched with items on IDEAS)

    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. 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. Philippe Mongin & Marcus Pivato, 2020. "Social preference under twofold uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 633-663, October.
    3. Stanca, Lorenzo, 2021. "Smooth aggregation of Bayesian experts," Journal of Economic Theory, Elsevier, vol. 196(C).
    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. Takashi Hayashi & Michele Lombardi, 2019. "Fair social decision under uncertainty and belief disagreements," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 775-816, June.
    6. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    7. Charles Blackorby & David Donaldson & Philippe Mongin, 2004. "Social Aggregation Without the Expected Utility Hypothesis," Working Papers hal-00242932, HAL.
    8. 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.
    9. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    10. Blackorby, Charles & Donaldson, David & Weymark, John A., 1999. "Harsanyi's social aggregation theorem for state-contingent alternatives1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 365-387, November.
    11. 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.
    12. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    13. Brandl, Florian, 2021. "Belief-averaging and relative utilitarianism," Journal of Economic Theory, Elsevier, vol. 198(C).
    14. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    15. Marc Fleurbaey, 2018. "Welfare economics, risk and uncertainty," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(1), pages 5-40, February.
    16. Marc Fleurbaey, 2010. "Assessing Risky Social Situations," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 649-680, August.
    17. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 427-452, July.
    18. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    19. 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.
    20. 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.
    21. Fleurbaey, Marc & Gajdos, Thibault & Zuber, Stéphane, 2015. "Social rationality, separability, and equity under uncertainty," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 13-22.

    More about this item

    Keywords

    Multiattribute utility; Separability; Subjective Probability; Harsanyi; Koopmans; Ex ante versus ex post welfare.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D57 - Microeconomics - - General Equilibrium and Disequilibrium - - - Input-Output Tables and Analysis
    • D60 - Microeconomics - - Welfare Economics - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ema:worpap:2014-15. 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: Stefania Marcassa (email available below). General contact details of provider: https://edirc.repec.org/data/themafr.html .

    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.