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cussed below, limits on actual desires via constraints of the concept of right are not allowed.)
§3. Points about Interpersonal Comparisons
(1) It is clear that the notion of summing up the pleasures (for simplicity) or degrees of happiness of different individuals presupposes that we have some way of comparing and estimating the pleasures experienced by distinct persons. We can say, for example, that individual A has twice the pleasures as individual B, etc.
Let us make a few observations about these points:
First, we assume that the ai’s are all equal and so let them be 1. This presumably is what Bentham meant (as quoted by Mill in Utilitarianism, Ch. V, par. 36) by: “everybody to count for one, nobody for more than one.” Mill interprets this weighting rule correctly: it does not imply, as Spencer argues in Social Statistics, an equal right to happiness; instead it follows from the independent definition of good as pleasure, or satisfaction, etc. As Mill says: it supposes only that equal amounts of happiness (pleasure) are equally desirable (good) whether felt by the same or different persons. All of this is implicit in the idea of measurement applied to pleasures. It is part of the principle of utility itself, not a premise needed to support it.15 So Mill says. This is fair enough given the understanding of good as pleasure (satisfaction) and nothing but pleasure. (Contrast Maine’s Brahmin, who would weight the pleasure of one who is a Brahmin 20 times that of those who are not; he needs to modify the strict classical principle in some way to reach his conclusion.)16
15.Mill says: “Mr. Herbert Spencer . . . says the principle of utility presupposes the anterior principle that everybody has an equal right to happiness. It may be more correctly described as supposing that equal amounts of happiness are equally desirable, whether felt by the same or different persons. This, however, is not a presupposition, not a premise needful to support the principle of utility, but the very principle itself; for what is the principle of utility if it be not that ‘happiness’ and ‘desirable’ are synonymous terms? If there is any anterior principle implied, it can be no other than this, that the truths of arithmetic are applicable to the valuation of happiness, as of all other measurable quantities.” Utilitarianism, ch. V, footnote to paragraph 36.
16.Henry Maine, Lectures on the Early History of Institutions (London: Murray, 1897), pp. 397ff.
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(2)Thus, henceforth, we assume that the weights are all = 1. We may add here that this is true of all individuals, however far distant in space or time; and since our actions are limited in their effects to the present or future, we can say (letting bygones be bygones) that the pleasures of all future persons have the same weights as those of present persons. There is then no pure time preference: this means that if we discount future pleasures, either our own or those of other people, this must be for some other reason than mere location in time or space alone; otherwise we apply the principle of utility incorrectly. For example, we must say: that some prospective pleasures are for various reasons more or less probable, their realization more or less uncertain. If so, they may be discounted, or weighted according to their estimated probability or likelihood; this gives the so-called mathematical expectation. But this form of discounting does not imply pure time preference: this discounting is based on reasonable estimates of uncertainty (probability) and not simply on the fact that a pleasure is distant (future) in time.
(3)Now for a few words about interpersonal comparisons. Evidently to arrive at interpersonal comparisons of utility we need two things at least:
(a)A cardinal measure of utility for each individual (all n of them) and
(b)A way of matching up the measures of utility of distinct individuals so that we can meaningfully relate and add: in short, we need correspondence rules that tell us how to compare and weight the pleasures of different persons.
To do (a) alone is not sufficient; only if we can do both (a) and (b), and do so in some satisfactory way, have we established a way to make interpersonal comparisons.
Some points about these cardinal measures: first, in the classical doctrine the individual cardinal measures of utility were based on individuals’ estimates of their own happiness arrived at by introspection and reflection and by their comparisons among their various states of well-being: the intensity and duration of their states of agreeable or disagreeable consciousness. In a word: individuals were thought (a) to be able to rank their various levels of well-being in a consistent way; they could also say (b) the difference between the levels of states A and B is equal to (or greater or less than) the difference between C and D. On these two assumptions, a cardinal measure for each individual does exist; and such a measure is independent from choices (preferences) involving risk or uncertainty. (Another pos-
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sible measure is based on a theory that goes back to Edgeworth; this measure too is independent from risks and uncertainty.)17 Thus the classical measure is not to be confused with the von Neumann–Morgenstern measure of utility, which is based on consistent choices over lotteries (various combinations of probability weighted alternatives). (Perhaps we can say more on this later.)18
Second, in setting up the correspondence rules so that we can add the utility measures of distinct individuals, it is not necessary that we be able to compare the levels (absolute levels) of the well-being of these individuals. Unit comparability suffices; level comparability is unnecessary. (Full comparability = level plus unit comparability.) Since we are maximizing the sum of well-being, all that matters is how much (by how many units) each individual goes up or down, from where they are, as a result of realizing the various feasible alternatives. Whether individual A, say, goes up or down n units from a level higher or lower than the level of B does not matter, assuming unit comparability. The institution or policy or action that leads to the largest net increase (balance of +’s and −’s) from the present situation will maximize utility over those alternatives.19
17. [In A Theory of Justice, rev. ed., section 49, p. 282, Rawls says the following: —Ed. “There are several ways of establishing an interpersonal measure of utility. One of
these (going back at least to Edgeworth) is to suppose that an individual is able to distinguish only a finite number of utility levels. A person is said to be indifferent between alternatives that belong to the same discrimination level, and the cardinal measure of the utility difference between any two alternatives is defined by the number of distinguishable levels that separate them. The cardinal scale that results is unique, as it must be, up to a positive linear transformation. To set up a measure between persons one might assume that the difference between adjacent levels is the same for all individuals and the same between all levels. With this interpersonal correspondence rule the calculations are extremely simple. In comparing alternatives we ascertain the number of levels between them for each individual and then sum, taking account of the pluses and minuses. See A. K. Sen, Collective Choice and Social Welfare (San Francisco: Holden-Day, 1970), pp. 93f; for Edgeworth, see Mathematical Psychics (London: Kegan Paul, 1888), pp. 7–9, 60f.”]
18.[See Rawls, A Theory of Justice, rev. ed., section 49, pp. 283–284, for a discussion of the von Neumann–Morgenstern definition of utility and problems with interpersonal comparisons of utility. —Ed.]
19.When economists speak of “adding utilities at the margin” they mean something like this, and precisely this if we suppose that the gains and losses (measured in goods and services) are sufficiently small so that the marginal utility of each individual stays approximately constant over the whole interval of possible gains and losses measured in goods and services, etc. [This sentence was crossed out in Rawls’s handwritten lecture notes. —Ed.]
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§4. Philosophical Constraints on a Satisfactory Measure of Interpersonal Comparisons
(1)There are at least two very important philosophical constraints on any satisfactory set of correspondence rules for interpersonal comparisons. Unless these are fulfilled, we have not yet defined a plausible utilitarian view. The first constraint is that the correspondence rules must be both meaningful and acceptable from the moral point of view as interpreted by the particular form of utilitarianism in question—in the present case, the strict classical doctrine. Not any kind of correspondence will be admissible. Moreover, all correspondence rules seem to involve some rather strong ethical assumptions, or at least assumptions with ethical implications, and these presuppositions must accord with the view in question.
(2)To illustrate: there is the well-known zero-one rule. This says: assuming that we have individual cardinal measures, and assuming that these measures are bounded above and below, pair these corresponding lower and upper bounds each with zero and one respectively. This sets up an interpersonal cardinal measure, but is it a measure we want? Does it define an aim that we want to maximize (given the utilitarian view)? Think about this in the light of the following extreme (and no doubt non-serious) example: this example has the merit of clearly exhibiting the difficulty. Consider a society that at time t0 consists of n people and m cats about equal in numbers (each person has their cat, as it were). Including all sentient beings, write: To maximize:
∑ ui = u1 + ... + un + un + 1 + ... + un + m
An amount of manna X falls each Hicksian week20 (time period): how to distribute it? Now, cats are more easy to get near the bliss point (u = 1) than people (adopting the 0–1 rule), let’s assume. So, perhaps over time, we maximize the sum of utilities by reducing the ratio of n/m so that at time t* (the optimum) there are relatively few people collecting and distributing the manna to lots of nearly blissfully happy cats. (I assume the amount of
20. [John R. Hicks (1904–1989), a British economist who won the Nobel Prize jointly with Kenneth Arrow in 1972. —Ed.]
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manna is fixed at X for all t.) The explanation of this conclusion is that cats are more efficient producers of utility per unit of X, if we use the 0–1 rule.
This example is not offered as a serious objection, but rather to bring home vividly the difficulty. Namely, just because we can establish some interpersonal measure so far proves nothing: this measure must define an aim that from a philosophical standpoint the theory says we should maximize, or one that we can live with. If the interpersonal measure has unacceptable implications, the utilitarian presumably has something else in mind. The point then is this: any scheme of correspondence rules has, it seems, ethical implications, (a) via the implications of the resulting principle, and (b) via the embedding of ethical notions in the correspondence rules; and it has ethical implications even if the scheme seems to involve no moral notions or principles. It has these implications because it sets up an aim that we are to maximize; and to maximize as the sole end of institutions and actions. Moreover, sometimes it may be clear that some ethical conceptions are embedded in the correspondence rules, e.g., is the 0–1 rule a way of saying that sentient beings have equal rights, or (perhaps better) equal claims to maximize satisfaction? For contrast this case with Mill’s reply to Spencer: that pleasures qua their intrinsic properties of intensity and duration (say) are equal regardless of whose pleasure they are. In the example above, we say simply: the total range of human pleasures (over all individuals) equals (by stipulation) the total range of feline pleasure (over all cats) regardless of variations between human individuals or between individual cats, or between cats and people. What justifies this stipulation? If we reject the 0–1 rule for cats and people, what is the correct ratio? Does the 0–1 rule hold for all people? Should we aim for simple pleasures, as the 0–1 rule implies?21
(3) Second, the correspondence scheme (for interpersonal comparisons) must not involve any ethical notions or principles that depend upon the notions of right or of moral worth. The reason for this is that the classical doctrine introduces the concept of right as that of maximizing some independently defined notion of good. (One clarifies this by giving examples: e.g., hedonism, human excellence, etc.)
We may have seen that the 0–1 rule may involve some ethical notion, for example of equal rights or equal claims to (maximized) satisfaction. Of
21. [See A Theory of Justice, rev. ed., pp. 284–285, for a related discussion of the value assumptions underlying interpersonal comparisons.]
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course, this is no objection to the view that uses the resulting principle; but what we need to be clear about is that this principle is no longer the classical principle of utility: it is something else. We introduced a principle of equal claims for all sentient (or human) beings; and where did we get that? Not from its being the best way to maximize utility; for we have used it in defining utility. So it is a basic first principle perhaps; if so, then this needs to be made explicit. Finally, why add utilities? Why not take the greater product of utilities, which normally results in less inequality in the distribution of utility?
(4)Again, the standard assumptions that utilitarian writers often use may be covert ways of introducing or adding first principles.22 This depends on how these assumptions are used and justified. If they are followed irrespective of the actual facts of individual psychology, then to this extent they are first principles; and mean in effect: always treat people as if these assumptions hold. If so, these first principles must be explicitly noted; and once again, we no longer have the strict classical doctrine.23
(5)Finally, a more subtle instance of the same problem is this: we must be careful to count among pleasures or satisfactions only states of consciousness or feelings that are suitably characterized: that is, solely by the good and by non-moral notions. Thus it is no argument against certain inequalities, say, from a utilitarian standpoint that people resent them; or that these inequalities make them indignant. For resentment and indignation are moral feelings: they imply that the individual affirms some conception of right and justice, etc., and presuppose a belief that the principles defining these conceptions are violated by these inequalities. Such an argument is
22.See Maine, Lectures on the Early History of Institutions, pp. 399f. [See A Theory of Justice, rev. ed., p. 285, where Rawls says the following of this same reference: —Ed.] “Maine’s assumptions on the standard utilitarian assumptions are apropos here. He suggests that the grounds for these assumptions are clear once we see that they are simply a working rule of legislation, and that this is how Bentham regarded them. Given a populous and reasonably homogeneous society and an energetic modern legislature, the only principle that can guide legislation on a large scale is the principle of utility. The necessity to neglect differences between persons, even very real ones, leads to the maxim to count all equally, and to the similarity and marginal postulates. Surely the conventions for interpersonal comparisons are to be judged in the same light. The contract doctrine holds that once we see this, we shall also see that the idea of measuring and summing well-being is best abandoned entirely.”
23.Cf. Lionel Robbins, The Nature and Significance of Economic Science (London: Macmillan, 1932), p. 141.
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not permitted by the constraints on the classical view. What a classical utilitarian must argue instead is that certain inequalities cause so much envy and anguish, or so much apathy and depression (all, say, unpleasant states of mind), that the greater balance of happiness is generally achieved by eliminating these inequalities. Even if we take these moral feelings into account, we are to weight them solely by their intensity and duration as feelings. Is that appropriate?
(6) A further example to illustrate the way in which moral notions may be included in individual utility functions is the following. Suppose we include a variable that represents individuals’ appraisal of, or attitude toward, the existing distribution of goods, or even of satisfaction (we assume that all individuals know what this distribution is). And assume that, for this purpose, the relevant feature of the existing distribution is based on the Ginicoefficient: each individual is pleased or displeased according to the degree of inequality as measured by this coefficient.24 They are more pleased as equality increases, ceteris parabis, although individuals may differ in the desire for equality. Then each ui looks something like this:
Ui = Ui (X, I, G) and so maximize ∑U i as defined
where X is a vector of goods; I is income; and G is the Gini-coefficient. Here we can assume that (to simplify) we have, for each individual, in-
difference curves something like those in Figure 10.
This scheme can fit into either an ordinal or coordinal theory. For our purposes here, let’s assume that the indifference curves have meaningful cardinal measures that mesh appropriately, via correspondence rules, with the measures of other individuals (interpersonal comparisons are valid).
Now the point is this: we can formally proceed to maximize the net balance of utility. But the theory is no longer teleological in the required sense:
(a)By including an entry for the Gini-coefficient, individuals take distri-
24.[The Gini-coefficient, attributed to Gini (1912), is a measure of inequality.
“There are various ways of defining the Gini coefficient, and a bit of manipulation . . .
reveals that it is exactly one-half of the relative mean difference, which is defined as the arithmetic average of the absolute values of differences between all pairs of incomes. . . .
Undoubtedly one appeal of the Gini coefficient, or of the relative mean difference, lies in the fact that it is a very direct measure of income difference, taking note of differences between every pair of incomes.” Amartya Sen, On Economic Inequality (Oxford: Oxford University Press, 1997), pp. 30–31.]
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bution into account. Offhand it looks as if they have a pattern principle of the first kind (a principle based on the pattern of distribution as represented by some property computed from the distribution of goods and income (the X’s and I’s)).
(b) We need to know on what basis individuals are really taking distribution into account. Is it really that their response to G is based on:
(i)benevolence and sympathetic temperament
(ii)moral convictions springing from a view of the duties of beneficence
(iii)convictions of justice in distribution; and of what conception more specifically
Figure 10.
EH curve = maximum output (given Gini-coefficient)a
So H = maximum output (over all Gini-coefficients)
So M = most preferred point (for individual i)b
a.[notes on the graph: E labels the point of intersection between the vertical axis and the EH curve; M labels the point of intersection between the EH curve and II; H labels the point of intersection between the EH curve and I. —Ed.]
b.Cf. William Breit, “Income Redistribution and Efficiency Norms,” in Hochman and Peterson, Redistribution Through Public Choice (1974).
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