Abstract
The naïve concept of social welfare as a sum of intuitively measurable and comparable individual cardinal utilities has been found unable to withstand the methodological criticism of the Pareto school. Professor Bergson2 has therefore recommended its replacement by the more general concept of. a social welfare function, defined as an arbitrary mathematical function of economic (and other social) variables, of a form freely chosen according to one’s personal ethical (or political) value judgments. Of course, in this terminology everybody will have a social welfare function of his own, different from that of everybody else except to the extent to which different individuals’ value judgments happen to coincide with one another. Actually, owing to the prevalence of individualistic value judgments in our society, it has been generally agreed that a social welfare function should be an increasing function of the utilities of individuals: if a certain situation, X, is preferred by an individual to another situation, y, and if none of the other individuals prefers Y to X, then X should be regarded as socially preferable to y. But no other restriction is to be imposed on the mathematical form of a social welfare function.
Journal of Political Economy, LXIII (1955), 309–321.
I am indebted to my colleagues at the University of Queensland, Messrs. R. W. Lane and G. Price, for helpful comments. Of course, the responsibility for shortcomings of this paper and for the opinions expressed in it is entirely mine.
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Notes
A. Bergson (Burk), ‘A Reformulation of Certain Aspects of Welfare Economics’, Quarterly Journal of Economics, LII (February, 1938), 310–34, and ‘
A. Bergson Socialist Economics’, in A Survey of Contemporary Economics, ed. H. S. Ellis (Philadelphia, 1949), esp. pp. 412–20.
M. Fleming, ‘A Cardinal Concept of Welfare’, Quarterly Journal of Economics, LXVI (August, 1952), 366–84. For a different approach to the same problem see L. Goodman and H. Markowitz, ‘Social Welfare Functions Based on Individual Rankings’, American Journal of Sociology, Vol. LVIII (November, 1952).
Of course, when I speak of preferences ‘from a social standpoint’, often abbreviated to ‘social’ preferences and the like, I always mean preferences based on a given individual’s value judgments concerning ‘social welfare’. The foregoing postulates are meant to impose restrictions on any individual’s value judgmements of this kind, and thus represent, as it were, value judgments of the second order, that is, value judgments concerning value judgments. Later I shall discuss the concept of ‘preferences from a social standpoint’ at some length and introduce the distinctive term ‘ethical preferences’ to describe them (in Sec. IV). But at this stage I do not want to prejudge the issue by using this terminology.
The more general term ‘utility distribution’ is used instead of the term ‘income distribution’, since the utility enjoyed by each individual will, in general, depend not only on his own income but also, owing to external economies and diseconomies of consumption, on other people’s incomes.
It is not assumed, however, that the other individuals are (like i and j) indifferent between X and X′ and between Y and Y′. In effect, were this restrictive assumption inserted into Postulate E, this latter would completely lose the status of an independent postulate and would become a mere corollary of Postulate D.
In view of consumers’ notorious ‘irrationality’, some people may feel that these postulates go too far in accepting the consumers’ sovereignty doctrine. These people may reinterpret the terms in the postulates referring to individual preferences as denoting, not certain individuals’ actual preferences, but rather their ‘true’ preferences, that is, the preferences they would manifest under ‘ideal conditions’, in posession of perfect information, and acting with perfect logic and care. With some ingenuity it should not be too difficult to give even some sort of ‘operational’ meaning to these ideal conditions, or to some approximation of them, acceptable for practical purposes. (Or, alternatively, these terms may be reinterpreted as referring even to the preferences that these individuals ought to exhibit in terms of a given ethical standard. The latter interpretation would, of course, deprive the postulates of most of their individualistic meaning.)
These postulates do not exclude, however, the possibility that such consideration may influence the relative weights given to different individuals’ utilies within the additive social welfare function. Even by means of additional postulates, this could be excluded only to the extent to which the comparison of individual utilities can be put on an objective basis independent of individual value judgments (see Sec. V).
See. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (2d ed.; Princeton, 1947), pp. 641 ff.
J. Marschak, ‘Rational Behavior, Uncertain Prospects, and Measurable Utility’, Econometrica, XVIII (1950), 111–41, esp. 116–21. Marschak’s postulates can be summarized as follows. Postulate I (complete ordering): The relation of preference establishes a complete ordering among all prospects. Postulate II (continuity): If prospect P is preferred to prospect R, while prospect Q has an intermediate position between them (being preferred to R but less preferred than P), then there exists a mixture of P and R, with appropriate probabilities, such as to be exactly indifferent to Q. Postulate III′ (sufficient number of nonindifferent prospects): There are at least four mutually nonindifferent prospects. Postulate IV (equivalence of mixture of equivalent prospects): If prospects Q and Q′ are indifferent, then, for any prospect P, a given mixture of P and Q is indifferent to a similar mixture of P and Q′, (that is, to a mixture of P and Q′ which has the same probabilities for the corresponding constituent prospects). Postulate I is needed to establish the existence of even an ordinal utility (or welfare) function, while the other three postulates are required to establish the existence of a cardinal utility (or welfare) function. But, as Postulates II and III are almost trivial, Postulate IV may be regarded as being decisive for cardinality as against mere ordinality.
There are reasons to believe that, in actuality, individual preferences between uncertain prospects do not always satisfy these postulates of rational behavior (for example, owing to a certain ‘love of danger’; see Marschak, op. cit., pp. 137–41). In this case we may fall back again upon the preferences each individual would manifest under ‘ideal conditions’ (see n. 7).
If we want a formal guaranty that no individual’s utility can be given a negative weight in the social welfare function, we must add one more postulate (for instance, Postulate D of Sec. II).
This principle is essentially identical with Professor Arrow’s ‘nondictatorship’ postulate in his Social Choice and Individual Values (New York, 1951), p. 30 (see also n. 14).
Mr. Little’s objection to Arrow’s nondictatorship postulate (see Little’s review article in the Journal of Political Economy, LX [October, 1952], esp. 426–31) loses its force, once the distinction between ‘ethical’ and ‘subjective’ preferences is noted. It does, then, make sense that an individual should morally disapprove (in terms of his ‘ethical’ preferences) of an unequal income distribution which benefits him financially, and should still prefer it (in terms of his ‘subjective’ preferences) to a more egalitarian one or should even fight for it—behavior morally regrettable but certainly not logically inconceivable. Arrow’s distinction between an individual’s ‘tastes’ (which order social situations only according to their effects on his own consumption) and his ‘values’ (which take account also of external economies and diseconomies of consumption and of ethical considerations, in ordering social situations) does not meet the difficulty, since it does not explain how an individual can without inconsistency accept a social welfare function conflicting with his own ‘values’. This can be understood only if his social welfare functions represents preferences of another sort than his ‘values’ do. (Of course, in my terminology Arrow’s ‘values’ fall in the class of ‘subjective’ preferences and not in the class of ‘ethical’ preferences, as is easily seen from the way in which he defines them.)
See my ‘Cardinal Utility in Welfare Economics and in the Theory of Risk-taking’, Journal of Political Economy, LXI (October, 1953), 434–35.
Or rather, if he had an equal chance of being ‘put in the place of’ any individual member of the society, with regard not only to his objective social (and economic) conditions, but also to his subjective attitudes and tastes. In other words, he ought to judge the utility of another individual’s position not in terms of his own attitudes and tastes but rather in terms of the attitudes and tastes of the individual actually holding this position.
Op. cit.
Obviously, the (unweighted or weighted) mean of the individual utilities defines the same social welfare function as their sum (weighted by the same relative weights), except for an irrelevant proportionality constant.
The concept of ethical preferences used in this section implies, of course, an ethical theory different from the now prevalent subjective attitude theory, since it makes a person’s ethical judgments the expression, not of his subjective attitudes in general, but rather of certain special unbiased impersonal attitudes only. I shall set out the philosophic case for this ethical theory in a forthcoming publication. (For an similiar view, see J. N. Findlay, ‘The Justification of Attitudes’, Mind, N.S., LXIII [April, 1954], 145–61.)
See I. M. D. Little, A Critique of Welfare Economics (Oxford, 1950), chap. iv. I have nothing to add to Little’s conclusion on the possibility of interpersonal comparisons of utility. I only want to supplement his argument by an analysis of the logical basis of such comparisons. I shall deal with the problem of comparisons between total utilities only, neglecting the problem of comparisons between differences in utility, since the social welfare functions discussed in the previous sections contain only total utilities of individuals.
Even identical preferences among uncertain prospects (satisfying the Marschak axioms) are compatible with different absolute levels of utility, since they do not uniquely determine the zero points and the scales of the corresponding cardinal utility functions.
By making a somewhat free use of Professor Carnap’s distinction, we may say that the assumption of different susceptibilities of satisfaction in this case, even though it would not be against the canons of deductive logic, would most definetely be against the canons of inductive logic.
See Little, A Critique of Welfare Economics, pp. 56–57.
On the reliability of comparisons between the utility of different situations before a change in one’s ‘taste’ (taken in the broadest sense) and after it, see the first two sections of my ‘Welfare Economics of Variable Tastes’, Review of Economic Studies, XXI, (1953–54), 204–8.
Though perhaps it would not be too difficult to reduce these margins quite considerably (for example, by using appropriate statistical techniques), should there be a need for more precise results.
Going back to our example, for instance, the disutility of labor and the utility of income are unlikely to be actually independent variables (as I have tacitly assumed), though it may not always be clear in which way their mutual influence actually goes. In any case, income is enjoyed in a different way, depending on the ease with which it has been earned, and labor is put up with in a different spirit, depending on the strength of one’s need for additional income.
This principle may be called the ‘principle of unwarranted correlation’ and is again a principle of inductive logic, closely related to the principle of unwarranted differentiation referred to earlier.
There is also another reason for which conclusions dependent on the principle of unwarranted correlation have somewhat less cogency than conclusions dependent only on the principle of unwarranted differentiation. The former principle refers to the case where two individuals differ in a certain variable X (in our example, in sex) but where there is no special evidence that they differ also in a certain other variable Y (in susceptibility to satisfaction). The latter principle, on the other hand, refers to the case where there is no ascertainable difference at all between the two individuals in any observable variable whatever, not even in X (in sex). Now, though the assumption that these two individuals differ in Y (in susceptibility to satisfaction) would be a gratuitous hypothesis in either case, obviously it would be a less unnatural hypothesis in the first case (where there is some observed difference between the two individuals) than in the second case (where there is none).
See L. Robbins, ‘Robertson on Utility and Scope’, Economica, N.S., XX (1953), 99–111, esp. 109; see also his An Essay on the Nature and Significance of Economic Science (2d ed.; London, 1948), chap.
See L. Robbins, vi; and his ‘Interpersonal Comparisons of Utility’, Economic Journal, XLIII (December, 1938), 635–41.
See Marschak’s discussion of what he calls ‘Ramsey’s norm’, in his paper on ‘Probability in the Social Sciences’, in Mathematical Thinking in the Social Sciences, ed. P. F. Lazarsfeld (Glencoe, Ill., 1954), Sec. I, esp. pp. 179–87; also reprinted as No. 82 of ‘Cowles Commission Papers’ (N.S.). For a survey of earlier literature see K. J. Arrow, ‘Alternative Approaches to the Theory of Choice in Risk-taking Situation’, Econometrica, XIX (October, 1951), 404–37, esp. 431–32, and the references there quoted.
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Harsanyi, J.C. (1980). Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility. In: Essays on Ethics, Social Behavior, and Scientific Explanation. Theory and Decision Library, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9327-9_2
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