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Social Choice with Interpersonal Comparisons

  • Equity, Arrow’s Conditions, and Rawls’ Difference Principle Econometrica 44 (1976), 793–804; reprinted in K.J. Arrow and G. Debreu (eds.), Landmark Papers in General Equilibrium Theory, Social Choice and Welfare (Edward Elgar, 2002), ch. 35, pp. 679–690; and (without appendix) in F.H. Hahn and M. Hollis (eds.), Philosophy and Economic Theory (Oxford University Press, 1979), ch. X, pp. 155–163.


    An Arrow social welfare function was designed not to incorporate any interpersonal comparisons. But some notions of equity rest on interpersonal comparisons. It is shown that a generalized social welfare function, incorporating interpersonal comparisons, can satisfy modifications of the Arrow conditions, and also a strong version of an equity axiom due to Sen. One such generalized social welfare function is the lexicographic form of Rawls’ difference principle or maximin rule. This kind of generalized social welfare function is the only kind satisfying the modified Arrow conditions, the equity axiom, and a condition which underlies Suppes’ grading principle. JSTOR link for paper

  • Why Ethical Measures of Inequality Need Interpersonal Comparisons Theory and Decision 7 (1976), 263–274.


    An ethical measure of income inequality corresponds to a social ordering of income distributions. Without interpersonal comparisons, the only possible social orderings are dictatorial, so there can be no ethical inequality measure. Interpersonal comparisons allow a very much richer set of possible social orderings, and the construction of ethical measures of inequality.

  • Equity in Two-Person Situations: Some Consequences Econometrica 47 (1979), 1127–1135.


    Suppose that social choice is based on interpersonal comparisons of welfare levels. Suppose too that, whenever all but two persons are indifferent between two options, a choice is made between these options which is equitable, in some sense. Then provided that individual welfare functions are unrestricted, and social choice is independent of irrelevant alternatives, it follows that social choice is always equitable, in the same sense. This applies when equity means satisfying Suppes’ indifference rule, or Suppes’ original justice criterion, or the lexicographic extension of Rawls’ difference principle. JSTOR link for paper

  • On Reconciling Arrow's Theory of Social Choice with Harsanyi's Fundamental Utilitarianism,” in G.R. Feiwel (ed.) Arrow and the Foundations of the Theory of Economic Policy (Macmillan and New York University Press, 1987), ch. 4, pp. 179–221. PDF copy

  • Independence of Irrelevant Interpersonal Comparisons Social Choice and Welfare 8 (1991), 1–19.


    Arrow’s independence of irrelevant alternatives (IIA) condition makes social choice depend only on personal rather than interpersonal comparisons of relevant social states, and so leads to dictatorship. Instead, a new “independence of irrelevant interpersonal comparisons” (IIIC) condition allows anonymous Paretian social welfare functionals such as maximin and Sen’s “leximin,” even with an unrestricted preference domain. But when probability mixtures of social states are considered, even IIIC may not allow escape from Arrow’s impossibility theorem for individuals’ (ex-ante) expected utilities. Modifying IIIC to permit dependence on interpersonal comparisons of relevant probability mixtures allows Vickrey–Harsanyi utilitarianism. PDF file of preprint

  • Interpersonal Comparisons of Utility: Why and how they are and should be made in J. Elster and J.E. Roemer (eds.), Interpersonal Comparisons of Well-Being (Cambridge: Cambridge University Press, 1991), ch. 7, pp. 200–254; reprinted in A.P. Hamlin (ed.) Ethics and Economics, Vol. I (Edward Elgar, 1996), ch. 22, pp. 410–464.


    A satisfactory complete normative criterion for individualistic ethical decision-making under uncertainty such as Harsanyi’s (Journal of Political Economy 1955) requires a single fundamental utility function for all individuals which is fully interpersonally comparable. The paper discusses reasons why interpersonal comparisons of utility (ICUs) have been eschewed in the past and argues that most existing approaches, both empirical and ethical, to ICUs are flawed. Either they confound facts with values, or they are based on unrealistic hypothetical decisions in an “original position”. Instead ICUs need to be recognized for what they really are — preferences for different kinds of people. PDF file of preprint

  • Harsanyi’s Utilitarian Theorem: A Simpler Proof and Some Ethical Connotations in R. Selten (ed.) Rational Interaction: Essays in Honor of John Harsanyi (Berlin: Springer-Verlag, 1992), pp. 305–319.


    Harsanyi’s utilitarian theorem states that the social welfare function is the weighted sum of individuals’ utility functions if: (i) society maximizes expected social welfare; (ii) individuals maximize expected utility; (iii) society is indifferent between two probability distributions over social states whenever all individuals are. After giving a simpler proof, an alternative axiomatic foundation for Vickrey–Harsanyi utilitarianism is provided. By making using an extended version of Harsanyi’s concept of a player’s “type” in the theory of games with incomplete information, the problem of forming social objectives when there is incomplete information can also be resolved, at least in principle. PDF file of preprint

  • Interpersonally Comparable Utility (with Marc Fleurbaey) in S. Barberà, P.J. Hammond, and C. Seidl (eds.) Handbook of Utility Theory, Vol. 2: Extensions (Boston: Kluwer Academic Publishers, 2004) ch. 21, pp. 1181–1285.


    This chapter supplements the earlier reviews in Hammond (1991a) and Suzumura (1996) by concentrating on four issues. The first is that in welfare economics interpersonal comparisons are only needed to go beyond Pareto efficiency or Pareto improvements. The second concerns the need for interpersonal comparisons in social choice theory, to escape Arrow’s impossibility theorem. The third issue is how to revise Arrow’s independence of irrelevant alternatives condition so that interpersonal comparisons can be accommodated. Finally, and most important, the chapter presents a form of utilitarianism in which interpersonal comparisons can be interpreted as ethical preferences for different personal characteristics.
    PDF file of preprint