The ignorant observer
Tóm tắt
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.
Tài liệu tham khảo
Anscombe F and Aumann R (1963). A definition of subjective probability. Ann Math Stat 34: 199–205
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
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
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
Chew S (1989). Axiomatic utility theories with the betweenness property. Ann Oper Res 19: 273–298
Cohen M and Jaffray J-Y (1980). Rational behavior under complete ignorance. Econometrica 48: 1281–1299
De Meyer B and Mongin P (1995). A note on affine aggregation. Econ Lett 47: 177–183
Dekel E (1986). An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom. J Econ Theory 40: 304–318
Dempster AP (1967). Probabilities induced by a multi-valued mapping. Ann Math Stat 38: 325–339
Dhillon A and Mertens J (1999). Relative utilitarianism: an improved axiomatization. Econometrica 67: 471–498
Diamond P (1967). Cardinal welfare, individualistic ethics and interpersonal comparison of utility: Comment. J Polit Econ 75: 765–766
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
Ellsberg D (1961). Risk, ambiguity and the Savage axioms. Q J Econ 75: 643–669
Epstein L and Segal U (1992). Quadratic social welfare functions. J Polit Econ 99: 263–286
Fishburn P (1970). Utility theory for decision making. Wiley, New York
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
Gilboa I and Schmeidler D (1989). Maximin expected utility with a non-unique prior. J Math Econ 18: 141–153
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
Harsanyi J (1955). Cardinal welfare, individualistic ethics and interpersonal comparisons if utility. J Polit Econ 63: 309–321
Harsanyi JC (1977). Rational behavior and bargaining equilibrium in games and social situations. Cambridge University Press, Cambridge
Jaffray J-Y (1989). Linear utility for belief functions. Oper Res Lett 8: 107–112
Karni E (1993). Subjective expected utility with state-dependent preferences. J Econ Theory 60: 428–438
Karni E (1998). Impartiality: definition and representation. Econometrica 66: 1405–1515
Karni E (2003). Impartiality and interpersonal comparisons of variations in well-being. Social Choice Welf 21: 95–111
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
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
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
Klibanoff P (2001). Characterizing uncertainty aversion through preference for mixtures. Social Choice Welf 18: 289–301
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
Luce RD and Krantz D (1971). Conditional expected utility. Econometrica 39: 253–271
Maskin E (1979). Decision-making under ignorance with implications for social choice. Theory Dec 11: 319–337
Milnor J (1954). Games against nature. In: Thrall, RM, Coombs, CH and Davis, RL (eds) Decision processes, pp 49–59. Wiley, New York
Mongin P (2001). The impartial observer theorem of social ethics. Econ Philos 17: 147–179
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
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
Nishimura KG and Ozaki H (2006). An axiomatic approach to \(\varepsilon\) -contaminationEcon Theory 27: 333–340
Rawls J (1971). A Theory of Justice. Harvard University Press, Cambridge
Rawls J (1974a). Concepts of distributional equity: some reasons for the maximin criterion. Am Econ Rev 64: 141–146
Rawls J (1974b). Reply to Alexander and Musgrave. Q J Econ 88: 633–655
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
Sen A (1976). Welfare inequalities and Rawlsian axiomatics. Theory Dec 7: 243–262
Shafer G (1976). A mathematical theory of evidence. Princeton University Press, Princeton
Skiadas C (1997a). Conditioning and aggregation of preferences. Econometrica 65: 242–271
Skiadas C (1997b). Subjective probability under additive aggregation of conditional preferences. J Econ Theory 76: 347–367
Vickrey W (1945). Measuring marginal utility by reaction to risk. Econometrica 13: 319–333
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
Weymark JA (2005). Measurement theory and the foundations of utilitarianism. Social Choice Welf 25: 527–555