Abstract
It is argued that Bayesian decision theory is a solution of an important philosophical problem, viz. the problem of how to define rational behavior under risk and uncertainty. The author has shown in earlier papers that if we take the Bayesian rationality postulates seriously, and take an individualistic point of view about social welfare, then our social welfare function must be a linear function of individual utilities: indeed, it must be their arithmetic mean. The present paper criticizes Diamond's and Sen's contention that one of the Bayesian postulates (viz. the sure-thing principle) does not apply to social decisions, even though it may apply to individual decisions. It also criticizes Sen's proposal of making social welfare a nonlinear function of individual utilities. The social welfare function proposed by the author depends on interpersonal utility comparisons. The use of such comparisons is defended. It is also argued that anybody who feels that the utilitarian (i.e., linear) form of the social welfare function is not egalitarian enough, should reject the author's individualism axiom, instead of trying to reject the Bayesian rationality axioms. However, this would be equivalent to giving egalitarian considerations a priority in many cases over humanitarian considerations. Finally, the paper discusses the reasons why even full agreement on the mathematical form of the social welfare function would not give rise to a Utopian state of moral consensus: moral controversies arising from disagreements about what predictions to make about future empirical facts would still remain.
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Bibliography
Carnap, Rudolf, Logical Foundations of Probability, University of Chicago Press, Chicago, 1950.
Diamond, Peter, ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility: A Comment’, Journal of Political Economy 75 (1967) 765–766.
Friedman, Milton and Savage, Leonard J., ‘The Utility Analysis of Choices Involving Risk’, Journal of Political Economy 56 (1948) 279–304.
Harsanyi, John C., ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-Taking’, Journal of Political Economy 61 (1953) 434–435.
Harsanyi, John C., ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’, Journal of Political Economy 63 (1955) 309–321.
Harsanyi, John C., ‘A General Theory of Rational Behavior in Game Situations’, Econometrica 34 (1966) 613–634.
Harsanyi, John C., ‘Can the Maximin Principle Serve as a Basis for Morality: A Critique of John Rawls's Theory’, American Political Science Review 69 (June 1975) 594–606.
Harsanyi, John C., ‘The Tracing Procedure: A Bayesian Approach to Defining a Solution for n-Person Noncooperative Games’, Parts I, II, Working Papers CP-359 and 360 (July 1974), Center for Research in Management Science, University of California, Berkeley. To appear in the International Journal of Game Theory.
Luce, R. Duncan and Raiffa, Howard, Games and Decisions, John Wiley, New York, 1957.
Marschak, Jacob, ‘Rational Behavior, Uncertain Prospects, and Measurable Utility’, Econometrica 18 (1950) 111–141.
Radner, Roy and Marschak, Jacob, ‘Notes on Some Proposed Decision Criteria’, in Robert M. Thrall et al. (eds.), Decision Processes, John Wiley, New York, 1954.
Rawls, John, ‘Justice as Fairness’, Philosophical Review 67 (1958) 164–194.
Rawls, John, A Theory of Justice, Harvard University Press, Cambridge, Mass., 1971.
Robbins, Lionel, ‘Interpersonal Comparisons of Utility’, Economic Journal 48 (1938) 635–641.
Sen, Amartya K., Collective Choice and Social Welfare, Holden-Day, San Francisco, 1970.
Sen, Amartya K., On Economic Inequality, Clarendon Press, Oxford, 1973.
Theil, Henri, Optimal Decision Rules for Government and Industry, North-Holland and Rand McNally, Amsterdam and Chicago, 1968.
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Harsanyi, J.C. Nonlinear social welfare functions. Theor Decis 6, 311–332 (1975). https://doi.org/10.1007/BF00136200
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DOI: https://doi.org/10.1007/BF00136200