Skip to main content
SpringerLink
Log in

The ignorant observer

  • Original Paper
  • Published:
Social Choice and Welfare Aims and scope Submit manuscript

Abstract

We propose an extension of Harsanyi’s Impartial Observer Theorem based on the representation of ignorance as the set of all possible probability distributions over individuals. We obtain a characterization of the observer’s preferences that, under our most restrictive conditions, is a convex combination of Harsanyi’s utilitarian and Rawls’ egalitarian criteria. This representation is ethically meaningful, in the sense that individuals’ utilities are cardinally measurable and fully comparable. This allows us to conclude that the impartiality requirement cannot be used to decide between Rawls’ and Harsanyi’s positions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anscombe F and Aumann R (1963). A definition of subjective probability. Ann Math Stat 34: 199–205

    Article  Google Scholar 

  • Arrow K and Hurwicz L (1972). An optimality criterion for decision making under ignorance. In: Carter, C and Ford, J (eds) Uncertainty and expectations in economics, pp 1–11. B. Blackwell, Oxford

    Google Scholar 

  • Castagnoli E, Maccheroni F, Marinacci M (2003) Expected utility with multiple priors. Proceedings of the third international symposium on imprecise probabilities and their applications, pp 121–132

  • Chateauneuf A (1991). On the use of capacities in modeling uncertainty aversion and risk aversion. J Math Econ 20: 343–369

    Article  Google Scholar 

  • Chew S (1983). A Generalization of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais paradox. Econometrica 51: 1065–1092

    Article  Google Scholar 

  • Chew S (1989). Axiomatic utility theories with the betweenness property. Ann Oper Res 19: 273–298

    Article  Google Scholar 

  • Cohen M and Jaffray J-Y (1980). Rational behavior under complete ignorance. Econometrica 48: 1281–1299

    Article  Google Scholar 

  • De Meyer B and Mongin P (1995). A note on affine aggregation. Econ Lett 47: 177–183

    Article  Google Scholar 

  • Dekel E (1986). An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. J Econ Theory 40: 304–318

    Article  Google Scholar 

  • Dempster AP (1967). Probabilities induced by a multi-valued mapping. Ann Math Stat 38: 325–339

    Article  Google Scholar 

  • Dhillon A and Mertens J (1999). Relative utilitarianism: an improved axiomatization. Econometrica 67: 471–498

    Article  Google Scholar 

  • Diamond P (1967). Cardinal welfare, individualistic ethics and interpersonal comparison of utility: Comment. J Polit Econ 75: 765–766

    Article  Google Scholar 

  • Drèze J (1987). Decision theory with moral hazard and state-dependent preferences. In: Drèze, J (eds) Essays on economic decisions under uncertainty, pp 23–89. Cambridge University Press, Cambridge

    Google Scholar 

  • Ellsberg D (1961). Risk, ambiguity and the Savage axioms. Q J Econ 75: 643–669

    Article  Google Scholar 

  • Epstein L and Segal U (1992). Quadratic social welfare functions. J Polit Econ 99: 263–286

    Article  Google Scholar 

  • Fishburn P (1970). Utility theory for decision making. Wiley, New York

    Google Scholar 

  • Gajdos T, Hayashi T, Tallon J-M, Vergnaud J-C (2007) Attitude toward imprecise information. mimeo, available http://eurequa.univ-paris1.fr/membres/tallon/GHTV-final.pdf

  • Gajdos T, Tallon J-M and Vergnaud J-C (2004). Decision making with imprecise probabilistic information. J Math Econ 40: 647–681

    Article  Google Scholar 

  • Gilboa I and Schmeidler D (1989). Maximin expected utility with a non-unique prior. J Math Econ 18: 141–153

    Article  Google Scholar 

  • Grant S, Kajii A, Polak B, Safra Z (2006) A generalized utilitarianism and harsanyi’s impartial observer theorem. Cowles Foundation Discussion Paper No. 1578, Yale University

  • Harsanyi J (1953). Cardinal utility in welfare economics and in the theory of risk-taking. J Polit Econ 61: 434–435

    Article  Google Scholar 

  • Harsanyi J (1955). Cardinal welfare, individualistic ethics and interpersonal comparisons if utility. J Polit Econ 63: 309–321

    Article  Google Scholar 

  • Harsanyi JC (1977). Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, Cambridge

    Google Scholar 

  • Jaffray J-Y (1989). Linear utility for belief functions. Oper Res Lett 8: 107–112

    Article  Google Scholar 

  • Karni E (1993). Subjective expected utility with state-dependent preferences. J Econ Theory 60: 428–438

    Article  Google Scholar 

  • Karni E (1998). Impartiality: definition and representation. Econometrica 66: 1405–1515

    Article  Google Scholar 

  • Karni E (2003). Impartiality and interpersonal comparisons of variations in well-being. Social Choice Welf 21: 95–111

    Article  Google Scholar 

  • Karni E (2006) Agency theory with maxmin expected utility players. mimeo, Johns Hopkins University, available at http://www.econ.jhu.edu/People/Karni/

  • Karni E (2007). Foundations of Bayesian theory. J Econ Theory 132: 167–188

    Article  Google Scholar 

  • Karni E and Safra Z (2000). An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory. J Math Econ 34: 315–327

    Article  Google Scholar 

  • Karni E, Schmeidler D (1981) An expected utility theory for state-dependent preferences. Working paper No. 48-40, Foerder Institute for Economic Research, Tel Aviv University

  • Karni E and Weymark JA (1998). An informationally parsimonious impartial observer theorem. Social Choice Welf 15: 321–332

    Article  Google Scholar 

  • Klibanoff P (2001). Characterizing uncertainty aversion through preference for mixtures. Social Choice Welf 18: 289–301

    Article  Google Scholar 

  • Kopylov I (2006) A parametric model of ambiguity hedging. mimeo, University of California at Irvine

  • Luce R and Raiffa H (1957). Games and decisions. Wiley, New York

    Google Scholar 

  • Luce RD and Krantz D (1971). Conditional expected utility. Econometrica 39: 253–271

    Article  Google Scholar 

  • Maskin E (1979). Decision-making under ignorance with implications for social choice. Theory Dec 11: 319–337

    Article  Google Scholar 

  • Milnor J (1954). Games against nature. In: Thrall, RM, Coombs, CH and Davis, RL (eds) Decision processes, pp 49–59. Wiley, New York

    Google Scholar 

  • Mongin P (2001). The impartial observer theorem of social ethics. Econ Philos 17: 147–179

    Article  Google Scholar 

  • Mongin P and d’Aspremont C (1998). Utility theory and ethics. In: Barberà, S, Hammond, P and Seidl, C (eds) Handbook of utility theory, I, pp 233–289. Kluwer, Dordrecht

    Google Scholar 

  • Moreno-Ternero J, Roemer J (2005) Objectivity, priority and the veil of ignorance. Discussion paper no. 2005-81, Center for Operation Research and Econometrics, Université Catholique de Louvain

  • Nehring K (2000). Rational choice under ignorance. Theory Dec 48: 205–240

    Article  Google Scholar 

  • Nishimura KG and Ozaki H (2006). An axiomatic approach to \(\varepsilon\) -contaminationEcon Theory 27: 333–340

    Article  Google Scholar 

  • Rawls J (1971). A Theory of Justice. Harvard University Press, Cambridge

    Google Scholar 

  • Rawls J (1974a). Concepts of distributional equity: some reasons for the maximin criterion. Am Econ Rev 64: 141–146

    Google Scholar 

  • Rawls J (1974b). Reply to Alexander and Musgrave. Q J Econ 88: 633–655

    Article  Google Scholar 

  • Schmeidler D (1984) Subjective probability and expected utility without additivity. IMA preprint series, University of Minnesota

  • Segal U (2000). Let’s agree that all dictatorship are equally bad. J Polit Econ 108: 569–589

    Article  Google Scholar 

  • Sen A (1976). Welfare inequalities and Rawlsian axiomatics. Theory Dec 7: 243–262

    Article  Google Scholar 

  • Shafer G (1976). A mathematical theory of evidence. Princeton University Press, Princeton

    Google Scholar 

  • Skiadas C (1997a). Conditioning and aggregation of preferences. Econometrica 65: 242–271

    Article  Google Scholar 

  • Skiadas C (1997b). Subjective probability under additive aggregation of conditional preferences. J Econ Theory 76: 347–367

    Article  Google Scholar 

  • Vickrey W (1945). Measuring marginal utility by reaction to risk. Econometrica 13: 319–333

    Article  Google Scholar 

  • Wang T (2003) Two classes of multiple priors. Discussion paper, Department of Finance, University British Columbia

  • Weymark JA (1991). A reconsideration of the Harsanyi-Sen debate on utilitarianism. In: Elster, J and Roemer, J (eds) Interpersonnal comparisons of well-being, pp 255–320. Cambridge University Press, Cambridge

    Google Scholar 

  • Weymark JA (2005). Measurement theory and the foundations of utilitarianism. Social Choice Welf 25: 527–555

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS–CES, 106-112 bd de l’Hôpital, 75647, Paris Cedex 13, France

    Thibault Gajdos

  2. CERC, 113 rue de Grenelle, 75007, Paris, France

    Feriel Kandil

Authors
  1. Thibault Gajdos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feriel Kandil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thibault Gajdos.

Additional information

We thank D. Bouyssou, A. Chateauneuf, M. Cohen, M. Fleurbaey, E. Karni, J.-F. Laslier, P. Mongin, J. Moreno-Ternero and especially J. Weymark, as well as seminar audiences at University Pompeu Fabra, University of Cergy-Pontoise, the Roy Seminar and RUD 2006 for useful comments. Comments by two anonymous referees have been extremely useful to improve the paper. Financial support from an ACI grant by the French Ministry of Research is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gajdos, T., Kandil, F. The ignorant observer. Soc Choice Welfare 31, 193–232 (2008). https://doi.org/10.1007/s00355-007-0274-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00355-007-0274-8

Keywords

Search

Navigation