Social preference under twofold uncertainty

  • Philippe MonginEmail author
  • Marcus Pivato
Research Article


We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as being objective and subjective, respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the two social welfare criteria, we present two compromises between them, one based on the ex ante criterion and absorbing as much as possible of the ex post criterion (Theorem 1), the other based on the ex post criterion and absorbing as much as possible of the ex ante criterion (Theorem 2). Both solutions translate the assumed Pareto conditions into weighted additive utility representations, as in Harsanyi’s Aggregation Theorem, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of the by now classic spurious unanimity argument and a novel informational argument labeled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms.


Ex ante social welfare Ex post social welfare Objective versus subjective uncertainty Objective versus subjective probability Pareto principle separability Harsanyi Social Aggregation theorem Spurious unanimity Complementary ignorance 

JEL Classification

D70 D81 



  1. Alon, S., Gayer, G.: Utilitarian preferences with multiple priors. Working paper version of Alon and Gayer (2016) (2014)Google Scholar
  2. Alon, S., Gayer, G.: Utilitarian preferences with multiple priors. Econometrica 84(3), 1181–1201 (2016)CrossRefGoogle Scholar
  3. Anscombe, F.J., Aumann, R.J.: A definition of subjective probability. Ann. Math. Statist. 34, 199–205 (1963)CrossRefGoogle Scholar
  4. Bewley, T.: Knightian decision theory. Part I. Decis. Econ. Financ. 25(2), 79–110 (2002)CrossRefGoogle Scholar
  5. Billot, A., Qu, X.: Utilitarian aggregation with reasonably heterogeneous beliefs. Working paper, Université Panthéon-Assas (Paris II) (2017)Google Scholar
  6. Billot, A., Vergopoulos, V.: Aggregation of Paretian preferences for independent individual uncertainties. Soc. Choice Welf. 47(4), 973–984 (2016)CrossRefGoogle Scholar
  7. Blume, L.E., Cogley, T., Easley, D.A., Sargent, T.J., Tsyrennikov, V.: A case for incomplete markets. Tech. rep., Reihe Ökonomie, Institut für Höhere Studien (2015)Google Scholar
  8. Brunnermeier, M., Simsek, A., Xiong, W.: A welfare criterion for models with distorted beliefs. Q. J. Econ. 129(4), 1753–1797 (2014)CrossRefGoogle Scholar
  9. Chambers, C., Hayashi, T.: Preference aggregation under uncertainty: Savage vs Pareto. Games Econom. Behav. 54, 430–440 (2006)CrossRefGoogle Scholar
  10. Chambers, C., Hayashi, T.: Preference aggregation with incomplete information. Econometrica 82(2), 589–599 (2014)CrossRefGoogle Scholar
  11. Clemen, R.T., Winkler, R.L.: Aggregating probability distributions. In: Edwards, W., Miles, R., von Winterfeldt, D. (eds.) Advances in Decision Analysis, pp. 154–176. Cambridge University Press, Cambridge (2007)CrossRefGoogle Scholar
  12. Crès, H., Tvede, M.: Regulation of trades based on differences in beliefs. Eur. Econ. Rev. 101, 133–141 (2018)CrossRefGoogle Scholar
  13. Danan, E., Gajdos, T., Hill, B., Tallon, J.-M.: Robust social decisions. Am. Econ. Rev. 106(9), 2407–2425 (2016)CrossRefGoogle Scholar
  14. Fishburn, P.C.: Utility Theory for Decision Making. Publications in Operations Research, vol. 18. Wiley, New York (1970)CrossRefGoogle Scholar
  15. Fleurbaey, M.: Welfare economics, risk and uncertainty. Can. J. Econ. 51(1), 5–40 (2018)CrossRefGoogle Scholar
  16. Fleurbaey, M., Mongin, P.: The utilitarian relevance of the social aggregation theorem. Am. Econ. J. Microecon. 8, 289–306 (2016)CrossRefGoogle Scholar
  17. Gayer, G., Gilboa, I., Samuelson, L., Schmeidler, D.: Pareto efficiency with different beliefs. J. Legal Stud. 43(S2), S151–S171 (2014)CrossRefGoogle Scholar
  18. Genest, C., Zidek, J.V.: Combining probability distributions: a critique and an annotated bibliography. Statist. Sci. 1, 114–148 (1986)CrossRefGoogle Scholar
  19. Gilboa, I., Samet, D., Schmeidler, D.: Utilitarian aggregation of beliefs and tastes. J. Polit. Econ. 112, 932–938 (2004)CrossRefGoogle Scholar
  20. Gilboa, I., Samuelson, L., Schmeidler, D.: No-betting Pareto dominance. Econometrica 82, 1405–1442 (2014)CrossRefGoogle Scholar
  21. Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2), 141–153 (1989)CrossRefGoogle Scholar
  22. Gorman, W.: The structure of utility functions. Rev. Econ. Stud. 35, 367–390 (1968)CrossRefGoogle Scholar
  23. Hammond, P.J.: Ex ante and ex post welfare optimality under uncertainty. Economica 48, 235–250 (1981)CrossRefGoogle Scholar
  24. Hammond, P.J.: Utilitarianism, uncertainty and information. In: Sen, A., Williams, B. (eds.) Utilitarianism and Beyond, pp. 85–102. Cambridge University Press, Cambridge (1983)Google Scholar
  25. Harsanyi, J.C.: Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J. Polit. Econ. 63, 309–321 (1955)CrossRefGoogle Scholar
  26. Hayashi, T., Lombardi, M.: Fair social decision under uncertainty and responsibility for beliefs. Econ. Theor. 67(4), 775–816 (2019)CrossRefGoogle Scholar
  27. Hild, M., Jeffrey, R., Risse, M.: Flipping and ex post aggregation. Soc. Choice Welf. 20, 267–275 (2003)CrossRefGoogle Scholar
  28. Keeney, R.L., Nau, R.: A theorem for Bayesian group decisions. J. Risk Uncertain. 43, 1–17 (2011)CrossRefGoogle Scholar
  29. Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York (1976). (Republished by Cambridge University Press, 1993)Google Scholar
  30. Mongin, P.: Consistent Bayesian aggregation. J. Econ. Theory 66, 313–351 (1995)CrossRefGoogle Scholar
  31. Mongin, P.: Spurious unanimity and the pareto principle. Tech. rep., THEMA, Université de Cergy-Pontoise, working paper. Published in 2016 in Economics and Philosophy 32, pp. 511–532 (1997)CrossRefGoogle Scholar
  32. Mongin, P.: The paradox of the Bayesian experts and state-dependent utility theory. J. Math. Econ. 29, 331–361 (1998)CrossRefGoogle Scholar
  33. Mongin, P.: Bayesian decision theory and stochastic independence. In: Lang, J. (ed.) Proceedings of TARK 2017 (2017)Google Scholar
  34. Mongin, P., Pivato, M.: Ranking multidimensional alternatives and uncertain prospects. J. Econ. Theory 157, 146–171 (2015)CrossRefGoogle Scholar
  35. Mongin, P., Pivato, M.: Social evaluation under risk and uncertainty. In: Adler, M.D., Fleurbaey, M. (eds.) Handbook of Well-being and Public Policy. Oxford University Press, Ch. 24, pp. 711–745 (2016)Google Scholar
  36. Nehring, K.: The veil of public ignorance. J. Econ. Theory 119, 247–270 (2004)CrossRefGoogle Scholar
  37. Posner, E., Weyl, G.: Fda for financial innovation: applying the insurable interest doctrine to twenty-first-century financial markets. Northwest. Univ. Law Rev. 107(3), 1307 (2013)Google Scholar
  38. Qu, X.: Separate aggregation of beliefs and values under ambiguity. Econ. Theory 63(2), 503–519 (2017). CrossRefGoogle Scholar
  39. Risse, M.: Bayesian group aggregation and two modes of aggregation. Synthese 135, 347–377 (2003)CrossRefGoogle Scholar
  40. Savage, L.J.: The Foundations of Statistics. Dover Publications Inc., New York (1972)Google Scholar
  41. Sen, A.K.: Social choice theory. In: Arrow, K.J., Intriligator, M. (eds.) Handbook of Mathematical Economics III. North-Holland, Amsterdam, pp. 1073–1181 (1986)Google Scholar
  42. Starr, R.M.: Optimal production and allocation under uncertainty. Quart. J. Econ. 87, 81–95 (1973)CrossRefGoogle Scholar
  43. Wakker, P.P.: Additive Representations of Preferences. Kluwer, Dordrecht (1989)Google Scholar
  44. Weymark, J.: A reconsideration of the Harsanyi-Sen debate on utilitarianism. In: Elster, J., Roemer, J. (eds.) Interpersonal Comparisons of Well-Being, pp. 255–320. Cambridge University Press, Cambridge (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.GREGHEC, CNRS and HEC Paris; LEMMA, Université Paris II Panthéon-Assas and Labex MME-DIIParisFrance
  2. 2.THEMA, Université de Cergy-PontoiseCergyFrance

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