UTILITARIANISM: OVERCOMING THE DIFFICULTY OF INTERPERSONAL COMPARISON

1. Introduction

Argenziano and Gilboa (2019; referred to as the AG paper below) obtain a very important result “that consumer choice data alone are sufficient … [to] provide a microfoundation for a weighted utilitarian social welfare function that reflects common moral intuitions about interpersonal comparisons of utilities” (abstract; order reversed). They also compare their assumptions and results with those of mine (Ng, 1975), apparently suggesting some problems of the latter. This paper makes a further comparison of the two results, showing the effective equivalence of the main results, despite the apparent opposite terminology, i.e., they call their result “weighted utilitarianism”, while I call mine “unweighted utilitarianism”. Their result is however stronger in the claim that consumer choice data alone are sufficient. However, this is at some costs of lesser generality of the (implicit) assumption/framework of individual preferences. Nevertheless, this limitation is not really important in affecting the acceptability of the utilitarian result itself, as argued below. Section 2 discusses the common elements of the two papers; Section 3 is on their differences; Section 4 discusses the sense of the adequacy of consumer data alone; Section 5 outlines a case for efficiency supremacy in specific issues, making the interpersonal comparisons of utility not needed for specific issues and simplifying economic policy formulation and implementation; Section 6 explains why the delay in the general acceptance of the compelling utilitarian results may be partly caused by some mistakes or misunderstandings.

2. Finite Sensibility and Utilitarianism: Weighted or Unweighted?

Let us start with the main common element of the two papers, the concept of a “just noticeable difference” (JND) used in psychology, and Edgeworth’s just perceivable increment of pleasure. While the latter is explicitly stated in subjective terms, the former may be interpreted either in terms of the objective quantities (like the amounts of goods consumed) or the subjective preferences or utilities (with utility taken as a representation of preference). Obviously, for a cup of coffee with two spoons of sugar, no one will be able to notice a difference if the amount of sugar differs by only a few molecules. However, while you may be indifferent between 2 (spoons of sugar) and 1.9, and also indifferent between 1.9 and 1.8, you may prefer 2 to 1.8. Thus, with finite sensibility, individuals are not perfectly discriminative and do not have an order (or weak order) over a convex set of consumption space (the minute indivisibility at the molecule or quantum level is ignored). Instead, the preference may be a semi-order with transitive preference but intransitive indifference. Based on this psychologically well-established fact, both papers obtain utilitarianism (defined as social welfare being the sum of individual utilities) under some compelling axioms.

The crucial axiom used in the AG paper is “Consistency” which basically, “states that if we focus on an individual i, and hold all other individuals” bundles fixed, society’s preferences are those of the individual. In case individual i expresses strict preference, say $x_i{P}_i{y}_i$, society agrees with that individual. Similarly, if individual i cannot tell the difference between $x_i$ and $y_i$, the difference between the two is immaterial to society as well’ (AG, 2019, p. 1517; where $P_i$ stands for the strict preference of individual i; I cannot find the exact symbol used for strict preference used by AG.)

Obviously, the acceptability of Consistency depends on the following implicit assumptions/simplifications:

For simplicity of reference, let us call these two assumptions together the “classical-private” simplification. Under this, the preference/utility of an individual depends only on her own consumption bundle. If the bundles of all individuals except i remain all unchanged, their utility levels also remain exactly unchanged under the simplification. Then, it is very reasonable that society’s preferences are those of this individual, making Consistency compelling. However, the need to adopt the classical-private simplification (i.e., the two assumptions above) seriously restricts the applicable scope of the analysis. It is true that much of the traditional economics, at least in its simplified, class-room version, already operates with these two simplified assumptions. Nevertheless, while this is true of much microeconomic analysis of the production and consumption of private goods, the traditional social choice and public choice literatures (e.g. Arrow, 1951/1963; Mueller, 2003) typically do not adopt either one of the above simplifications. An alternative or social state x is typically interpreted to include all relevant aspects that may affect the preference of any individual and include “a complete description of the amount of each type of commodity in the hands of each individual, the amount of labor to be applied by each individual, the amount of each productive resource invested in each type of productive activity, and the amounts of various types of collective activity such as municipal services, diplomacy and its continuation by other means, and the erection of statues to famous men” (Arrow, 1951/1963, p. 17). In addition, the preference of an individual is taken to be possibly affected by all aspects of a social state, not just confined to her own consumption bundle. Thus, the traditional social choice framework does not adopt the classical-private simplification. Without this simplification, Consistency is not acceptable as, even if we hold the private consumption bundles of all individuals except that of i unchanged, (1) changes in the consumption bundle of this individual may affect the utilities of other individuals through external effects, relative comparison effect, caring effects, etc.; (2) changes in public goods and/or non-economic factors may also affect individual utilities. Then, the society’s preference should not just depend on that of individual i only.

Under the classical-private simplification, Consistency is compelling. This is so since, if the consumption bundles of all individuals except i are held fixed, the utility levels of all these non-i individuals are unchanged under the classical-private simplification. Then, requiring that the society’s preference be in accordance with that of individual i is similar to the Pareto principle and very compelling. For those who find the classical-private simplification acceptable, or for those who confine the analysis to those changes satisfying the simplification, Consistency should be regarded as compelling and the AG utilitarianism result should be accepted. In fact, I wish to go a bit further in supporting AG on this.

The classical-private simplification is not something very contrived, but a very familiar simplified framework much analyzed and taught by economists. If the acceptability of utilitarianism is compelling in this framework, there seems to be no relevant consideration that makes it unacceptable to a more general framework where the classical-private simplification may not hold. For example, we may reason this way. The classical simplification and Consistency suggest that, where all individuals except i have unchanged utility levels, the social preference should be in accordance with that of this particular individual i only. This point should be independent of whether the unchanged utility levels are obtained through the classical-private simplicity plus Consistency or through other offsetting changes in objective states such as making all utility levels unchanged except one individual. The acceptability should remain unchanged. This acceptability, plus the recognition of the fact (proven by psychological studies) of the finite sensibility of all individuals, leads us to a utilitarian social welfare function (SWF), if each individual utility level is calibrated in accordance with the just perceivable level of pleasure in subjective terms or a JND in objective ones. Then, it follows that this utilitarianism result is not just confined to the framework where the classical-private simplification applies. It should apply generally.

Using this principle that we support the more general applicability of the AG utilitarianism result, we may also show that some problems that AG argue to be applicable to my way of supporting utilitarianism are not really problems or that they are also applicable to the AG way. Similarly, when extended to be applicable to the general social choice framework (i.e., without the classical-private simplification), the sufficiency of consumer choice data alone no longer applies. These considerations make the AG result not that much different from my result in the general framework. However, when confined to the classical-private simplification, the sufficiency of consumer choice data is an important result.

We may also obtain the more general (beyond the classical-private simplification) applicability of the utilitarianism result by replacing AG’s original Consistency by Consistency’. Consistency’: If we focus on an individual i, and hold all other individuals’ utility levels exactly fixed, society’s preferences are those of the individual. In case individual i expresses strict preference, say $x_i{P}_i{y}_i$, society agrees with that individual. Similarly, if individual i cannot tell the difference between $x_i$ and $y_i$, the difference between the two is immaterial to society as well. In other words, Consistency’ simply replaces fixed bundles of all non-i individuals by fixed utility levels. With the classical-private simplification, the fixation of bundles implies the fixation of utility levels. Since economists (especially those interested in the welfare, social choice, and economic policy areas) after the neoclassical revolution are more interested in individual preferences than in the objective quantities of consumption, Consistency’ should be more appealing than Consistency. With Consistency’, the proof of the AG utilitarian result follows exactly the same way except for the replacement of the fixation of bundles by the fixation of utility levels. As Consistency’ is not confined to the classical-private simplification, the resulting AG’ utilitarianism is similarly not so confined.

Before discussing the differences between the two approaches in the next section, let us first clarify the point regarding weighted versus unweighted utilitarianism. Formally, weighted utilitarianism has the SWF as: $W=a_1{u}_1+a_2{u}_2+\cdots +a_n{u}_n$, where W is the social welfare, $a_i$ is the weight for individual i, $u_i$ is the utility level of individual i, and n is the number of individuals. On the other hand, unweighted or equally-weighted utilitarianism has all the $a_i$ equal over all individuals (usually also equal one without loss of generality). Under both the AG and my results, each just perceivable amount of happiness or JND for any individual should have the same significance on social welfare or social preference. Holding all other individual utility levels unchanged (all individuals strictly indifferent intrinsically¹), one JND of (any) one individual or one just perceivable amount of happiness of any individual should cause a just perceptible social preference (Consistency’). If we also use the convention of having one to stand for a just perceptible social preference, then the SWF must be in the form of an unweighted sum of individual utilities, if the utility functions of all individuals also conform to the standardization of using one util for a “marginal preference” in preference terms, or a just perceivable increment of happiness in subjective happiness terms. On the other hand, if we do not so standardize all individual utility functions, such that a utility difference of more than ${\delta }_i$ gives rise to preference (and indifference otherwise) for individual i, with ${\delta }_i$ possibly differing over different individuals, we must “weight” these individual utility indices by the inverse of ${\delta }_i$ so as to conform to the equal social welfare significance of each individual just perceivable increment. This approach (possibly differing ${\delta }_i)$ is used by AG, thus making their result that of weighted utilitarianism. On the other hand, I use the standardization of one util for one marginal preference (or maximal indifference rather, given the continuity of preference on a technical reason²) or a just perceivable increment of happiness for all individuals. Thus, I obtain unweighted utilitarianism. Noting the different standardization, the two results are really the same in their effective conclusion. We should both have unweighted (or equivalently, equally weighted) utilitarianism, if we both use my standardization. Thus, the apparent difference between weighted and unweighted utilitarianism involves really no difference in substance at all, since the standardization is a pure normalization with no substantive differences.

3. The Differences Between Ng (1975) and Argenziano and Gilboa (2019)

We now come to AG’s comparison of the main axioms that they and I use to get our utilitarian results, namely their Consistency and my Weak Majority Preference (renamed Majority Weak Preference or MWP by AG). The latter “states that, if there is a weak majority of individuals who strictly prefer one alternative over another, while no individual has the opposite preference, society should respect the majority preference” (AG, 2019, p. 1523). Here, “weak majority” requires “at least 50%”.³ AG mention three “points” (that probably appear to readers as “problems”) of MWP that are not involved with Consistency.

First, “The MWP axiom involves counting individuals. The theorem shows that adding up individuals in each of two sets (those who prefer an alternative x to y and those who do not) eventually leads to adding up the utilities of the individuals. This is far from trivial, but from a conceptual viewpoint it feels as if addition is explicitly assumed” (AG, 2019, p. 1523). For the “theorem” part, apart from the no-difference-in-substance of the opposite naming as explained above, the two results are exactly the same, if “addition” (or anything else) is involved in my result, so is that in the AG result. For the axiom parts, there could be some differences. MWP “involves counting individuals”; Consistency involves not only the classical-private simplification as discussed above, it also involves ensuring that the private bundles of all individuals except i remain identical.

Second, “The MWP axiom involves counting by size of the utility difference. To identify the two sets of individuals to be counted (those who prefer an alternative x to y and those who do not), the axiom requires to count how many utility differences are above the individual JND and how many are below it — and thus the intuition behind the axiom seems to directly appeal to the additive form we would like to derive” (AG, 2019, p. 1523). The meaning of this quoted passage is unclear to me. First, AG may not (as I first thought) mean that MWP counts the size or number of just noticeable utility differences, but just mean the counting of the numbers of two sets of individuals, one set having a strict preference and one set not so having. It seems that having to count the number of individuals in the two sets is no big deal; most voting methods involve counting those in favor and those against. Moreover, in comparison, Consistency involves ensuring that the consumption bundles of all individuals except one remain exactly unchanged, obviously a much more demanding exercise than counting the number of two sets of individuals. On the other hand, AG may mean that MWP does count the size or number of just noticeable utility differences, which is consistent with their claim of “directly appeal to the additive form we would like to derive”. But this is not true. Only the resulting theorem on utilitarianism involves this counting; MWP itself only counts the numbers in the two sets of individuals. The utilitarianism result of AG also involves this counting.

Third, “The MWP axiom allows society to penalize an individual in a way that favors others, as long as this is unnoticeable by the individual. Suppose there are only two individuals, and consider a donation scheme similar to the one we discussed in Section 3: one cent is transferred from j to i. Assume this makes a noticeable difference for i, but not for j. The MWP axiom implies that society should approve such a transfer, because one JND is being gained and none is being lost. As we discussed in Section 3, such a transfer involves a feeling of deception, and assuming that society approves it might not capture common moral sentiments” (AG, 2019, p. 1523). Some discussion of this “objection” is needed.

“The MWP axiom implies that society should approve such a transfer” mentioned above only if transfer costs, disincentive effects and possibly other undesirable effects are absent or offset by other benefits. If this qualification is satisfied, such a transfer is actually socially desirable, and will also be approved by AG’s utilitarianism result. Transfers that involve a feeling of deception and not capturing common moral justification discussed in AG’s Section 3 are such as “a suggestion that each individual $j\ne i$ contribute 1 cent to i. Assume that 1 cent is a small enough quantity for each $j\ne i$ not to notice it. By contrast, the accumulation of these cents can render i rich” (AG, 2019, p. 1517). However, such a scheme is not supported by MWP as that scheme makes only one person noticeably better off and all others unnoticeably worse off, while MWP requires making at least 50% of individuals noticeably better off.

Whether we use my MWP or AG’s Consistency under the classical-private simplification, we get the utilitarianism result. Then, in applying this result to evaluate policies/changes, either approach will involve the counting of utility differences (or the number of JNDs or marginal preferences) and will also approve a transfer that make any one person noticeably better off and one person unnoticeably worse off, with all other individual utilities remaining exactly unchanged, after accounting for all transfer costs, disincentive effects, etc. There is no difference in the result. Thus, the main differences between the two approaches are:

The classical-private simplification, though rather restrictive from a social choice perspective, is much used in economic analysis. Moreover, as argued above, once we see the compellingness of the utilitarianism result under the classical-private simplification, there seems to be no reason to deviate from this result even when we deal with the general social choice framework. On the other hand, if we use Consistency’ instead of Consistency, this AG’ result does not require the classical-private simplification. But on the other hand, the sufficiency of consumer data alone cannot be claimed. The sense in which consumer data alone are sufficient is discussed in the next section.

4. The Sufficiency of Consumer Data Alone

Under the classical-private simplification and finite sensibility, Consistency is compelling. Remarkably, under this compelling axiom alone, AG derive the utilitarianism result. The rigorous proof has already been provided by AG. Here, we give an intuitive explanation why the result follows and then the meaning of the sufficiency of consumer data alone. This intuitive explanation also shows why we may use Consistency’ to replace Consistency and dispense with the classical-private simplification.

Under the classical-private simplification, if we hold the private bundles of all individuals except person i fixed, their intrinsic preferences and hence their utility levels are also held fixed. Then, it is compelling that social preferences agree with that of person i. Under finite sensibility, any individual i is not perfectly discriminative. Her preference is not an order; at most, it is a semi-order. Then if the difference in her own bundle is not large enough to generate a just perceivable increment of pleasure, she will remain indifferent. And so is the society under Consistency. Whenever she perceives a noticeable increment, so must the society. Thus, if we use for simplicity (but without loss of generality) the standardization of using the utility number of one for each and every individual just imperceptible indifference (continuous with a just perceptible preference) and also the welfare number of one for a social welfare increment resulting from the increase in the utility level of one single individual by one, holding the utility levels of all other individuals exactly unchanged, the resulting social welfare W must increase one unit by one unit as the utility level of any individual increases also one unit by one unit. Otherwise, Consistency will be violated. Consistency is required for any individual i, hence social welfare W must behave so (increases one unit by one unit as …) for each and every individual. Moreover, this must be so whatever the utility levels of all other individuals are, as long as their own bundles are held exactly unchanged (or if their utility levels are held exactly unchanged under a more general framework beyond the classical-private simplification as is the case where Consistency’ is used instead of Consistency). Thus, it must be the unweighted sum of individual utilities. While this utilitarian result is remarkable under Consistency, AG’s paper may be more important due to the sufficiency of consumer data alone for this. However, this sufficiency needs to be recognized correctly.

Economists “implicitly agree with the claim that consumer choice data alone do not provide scientific, empirical grounds for interpersonal comparisons of utility. … Our article points out that this perception is false, because actual consumer choice data, even under certainty, contain much more information than the idealized classroom model assumes. In particular, they contain information that makes it possible, at least in principle, to compare utility differences across individuals on a scientific basis” (AG, 2019, p. 1512). This in-principle possibility is obviously valid. As stated in Consistency and supported by psychological studies, small enough variations in one’s bundle will not generate noticeable differences. The JNDs then give rise to interpersonal comparable utils under Consistency. Thus, the sufficiency of consumer data alone for proving the utilitarian result as used by AG is valid under the classical-private simplification.

Once we obtain the utilitarian result (which is the same across Bentham, Edgeworth, Ng, and AG) and wish to apply it to evaluate actual policies/changes, using consumer data alone is usually insufficient for most cases. Of course, for cases satisfying the Pareto principle, we have no problems. However, most changes needing evaluation involve non-Pareto changes and interpersonal comparisons of utility gains and losses are needed. For those changes satisfying the classical-private simplification, in principle, we may obtain such comparisons by varying the private consumption bundles alone and finding out the preferences and indifferences. However, market consumption (and production) data alone are usually not fine enough to generate such comparisons. Some experimental investigations may be needed. The adequacy of consumer data alone should be understood in this light.

For changes beyond the classical-private simplification (i.e., where non-self-centered preferences are involved or where variation in non-private or non-economic variables are involved), it may be thought that consumer data alone cannot be enough. However, this does not mean that no comparisons are possible, as experimental investigations may be combined with indirect comparisons (Ng, 1975, Section 9), making the required comparisons still possible, though possible lack of information and practical difficulties may be involved.

5. No Need for Interpersonal Utility Comparisons Under Efficiency Supremacy in Specific Issues

There is another quite different consideration making the issue of practical interpersonal comparisons of utility gains and losses much less of a problem. In specific issues on the desirability of a social policy/change or a cost-benefit analysis of a certain project, we should follow the principle of efficiency supremacy and treat a dollar as a dollar in either costs or benefits whether for the rich or for the poor, leaving the objective of promoting equality to the general equality promotion policies (including taxes/subsidies). This is so because this is a more efficient way that allows the society to achieve any degree of equality at lower efficiency costs, or at any given efficiency costs, it allows us to achieve a higher degree of equality.

Suppose that a project (together with its financing) involves making the poor worse off by $5 million but the rich better off by $8 million in net terms. The efficiency supremacy policy (which maximizes aggregate unweighted net gains and losses in monetary terms) dictates the acceptance of the project. It may be quite true that the loss of $5 million by the poor may be larger than the gain of $8 million by the rich in utility terms. However, if in the long run, the efficiency supremacy policy is complemented by some appropriate equality promotion policy, a higher tax of $7 million on the rich and a higher subsidy to the poor of $6 million would involve making all groups better off overall. It may be thought that this ignores the fact that the more progressive tax/subsidy required will generate disincentive effects, possibly more than offsetting the net gains of the project/change. This reasoning ignores the crucial point that the extent of the disincentive effects should be a function not just of the tax-transfer scheme but also other aspects of redistribution, including the use of distributional weights in specific issues to promote equality. The policy to reject the above-mentioned project ($+$$8 million for the rich and −$5 million for the poor) also generates disincentive effects, offsetting the disincentive effects of the changes in tax transfer. In addition, such efficiency-inconsistent policies have additional efficiency costs, and hence are inferior to the promotion of equality through the general policy instead of tempering with specific issues. This is true unless the tempering is justified on some efficiency grounds like external effects, but in this case, it is not regarded as efficiency-inconsistent, and a policy of efficiency supremacy in specific issues does not exclude it. (See Ng, 1984 for a demonstration of this as well as some complications involved.)

Given the superiority of the efficiency supremacy policy in specific issues, we then do not have to make interpersonal comparisons of utility gains and losses in specific issues; we just aggregate gains and losses measured in monetary terms (which do not need interpersonal comparisons of utility) and decide in accordance to aggregate net benefits. This is actually the same as Harberger’s (1971) first basic postulate of applied welfare economics. However, Harberger did not provide a justification that following this postulate (or our efficiency supremacy policy in specific issues) will be Pareto optimal as shown in Ng (1984).⁴

Even under the efficiency supremacy policy in specific issues, interpersonal comparisons of utility are not completely unnecessary. This is so because in deciding the appropriate degree of progressivity in the general equality promotion policy, the interpersonal comparisons of utility are still needed. However, Harberger’s first postulate or our efficiency supremacy policy in specific issues frees us from having to make these difficult interpersonal comparisons of utility gains and losses in each specific issue or policy. This provides a tremendous simplification in public policies in general and in cost-benefit analysis in particular.

6. The Misguided Suspicion of Utilitarianism

AG also “speculate about the reasons that this point has not been accepted by the profession following Ng (1975) and Edgeworth (1881)” (AG, 2019, p. 1524). Here, a brief note on this is given.

First, it should be noted that, when we write social welfare W as a function of individual utility levels, many simplifications are involved. First, we ignore the possible divergences between individual utilities (representing preferences) and individual welfare (or happiness), as discussed in Ng (1999). Where (individual) preference and welfare diverge, ultimately speaking, I am personally in favor of using welfare, though the possible unfavorable effects (ultimately on individual welfare levels) of diverging from following individual preferences should be taken into account. However, this complication needs not detain us here.

Second, the utility levels of all relevant individuals should obviously enter the social welfare function. This should include individuals in the future as the real world does not vanish after this period. However, for simplicity, much economic, and especially welfare-economic, the analysis uses an a-temperal framework. Thus, the n individual utility levels in the social welfare function include both the present and future individuals. Then, if an analysis is complete, all effects inclusive of transfer costs, disincentive effects, social harmony effects, morality effects, etc. that may affect individual utility/welfare levels now and the future should be taken into account. Explicit/additional discounting needs not be involved if the individual utility/welfare levels are already taken as the certainty equivalent level, or already discounted by the uncertainty of realization.

Third, due to the diminishing marginal utility of income, a dollar is worth much more when one is poor than when one is rich. This makes risk aversion with respect to incomes and other material things rational (or expected-utility maximizing; Ng, 1984). Ignoring interpersonal differences, a dollar of the poor is worth much more than a dollar of the rich. If factors like social harmony, crime-reduction, etc. are separately dealt with as discussed in the previous paragraph, this makes the diminishing marginal utility of income/consumption the only factor accounting for the point that the society should put more emphasis in evaluating the incomes of the poor than those of the rich, at least in the absence of additional justifications (which would in any way all violate MWP and Consistency and not really ethically acceptable). Then, while social welfare should be concave in terms of individual income levels, it should be linear in terms of individual utility/welfare levels. Given anonymity, it should be (unweighted) utilitarian.

The main objection to the utilitarian SWF is the intuitive inclination to put more weight on not only the income levels of the poor, but also on the utility levels of the less well-off. This intuition is partly due to our inborn inclination in favor of equality which favors cooperation that helped our survival, and partly due to the social/cultural climate that also favors equality. However, while this intuition is valid as applied to income levels, it involves some form of double discounting when applied to the utility/welfare levels. When we put social welfare as a function of individual utility/welfare levels instead of consumption/income levels, we already implicitly discount the income levels of the rich due to the diminishing marginal utility of income. The utility levels of the rich/better-off should not be further discounted again. Consideration such as the crime reduction effects, social harmony effects, etc. should be dealt with by considering how they affect individual utility/welfare levels, now and in the future, and be incorporated through their effects on the various utility/welfare levels. (For a further argument in favor of welfarism and against Kantian and Rawlsian arguments, see Ng, 2019, Appendix B.)

Ignoring the differences between individual utility and welfare levels, utilities are already the ultimate objective of individuals. Then, under the Fundamental Value Proposition of Individual Preferences (social welfare must be based on individual preferences; Bergson, 1938), individual utilities must also be the ultimate objective of society. Then, since by definition, we cannot have the diminishing marginal utility of utility (the marginal utility of utility is identically equal to one), we must not give a lower weight to the marginal utility of a higher utility level, as is so in a strictly concave SWF. The intuition in favor of such an SWF and against the utilitarian one is misguided and also violates the compelling MWP and Consistency. The general acceptance in social choice and public policy⁵ of the interpersonally comparable cardinal utility and the utilitarian result (social welfare is an unweighted sum of individual utilities) of Bentham–Edgeworth–Ng–Argenziano–Gilboa is long overdue.

Acknowledgment

I wish to thank Rossella Argenziano and Itzhak Gilboa for reading the paper and confirm that it is “very interesting and it does indeed clarify the relationship between our two results”.

ORCID

Yew-Kwang Ng  https://orcid.org/0000-0001-5669-9883

Notes