B.M.S. Van Praag: The Relativity of the Welfare Concept
B.M.S. Van Praag: The Relativity of the Welfare Concept
Abstract and Keywords
Osmani takes up a question which relates to a potential application of van Praag's approach: how well can individual utilities, as measure by van Praag, serve as the basis of social welfare evaluation? Osmani demonstrates that the concept of interpersonally comparable utility has an empirical basis by examining closely the concept of utility that emerges from van Praag's method of measurement. While accepting that van Praag's utility numbers have the property of interpersonal comparability, Osmani doubts that these numbers represent the concept of individual welfare that is relevant for building a social welfare function.
Professor van Praag's paper presents in a distilled form the outcome of two decades of research on a novel approach to the evaluation of individual welfare. The basic tool is an ‘income evaluation questionnaire’ in which people are asked to mention the income levels which in their own judgement correspond to certain prespecified verbal labels such as ‘good’, ‘bad’, ‘sufficient’, etc. This information is then used to develop an interpersonally comparable measure of utility.
Over the years, van Praag and his colleagues have strengthened the foundations of this approach and applied it to a wide variety of issues concerning social policy and social assessment. In their expert hands, the approach has proved amazingly versatile. Van Praag gives a flavour of this versatility by either discussing or referring to many of the applications of the approach. There is, however, one potential application which is not taken up in his paper but which is especially germane to the context of the present volume. It relates to the question: how well can individual utilities, as measured by van Praag, serve as the basis of social welfare evaluation? This question is motivated by van Praag's resurrection of interpersonally comparable utility. While elaborating the mainstream approach to utility, van Praag rightly reminds us that with the denial of interpersonal comparability of utility in the 1930s, welfare economics lost much of its power to compare the goodness of alternative social states. However, as he again correctly notes, several economists, especially those interested in the issues of inequality and poverty, continued to develop the framework for making social welfare judgements by assuming comparability of individual welfare. In doing this, these economists were, in the words of van Praag, ‘building the first floor when the foundations are not yet laid’. This is because the underlying presumption of comparable utility remained to be established. Van Praag does not object to this method, for he is quite willing to accept comparable utility as a primitive concept if that is what is needed to make meaningful social welfare judgements, but notes that it would nevertheless ‘be nice if we could find some credible method of getting evidence on utility’. This is precisely what he claims to have done; as he says, ‘The main message of the paper is then that from attitude questions an ordinal but interpersonally comparable individual welfare concept may be constructed which is “operationally useful’ ”.
One is therefore led to ask: can the van Praag utilities, interpersonally comparable as they are, serve as the missing foundation of social welfare evaluation? The paper explicitly avoids pursuing this question, being content merely to (p.387) demonstrate that the concept of interpersonally comparable utility has an empirical content. But this is the question I wish to examine here, thus going beyond the paper itself, but building on its empirical findings. My method is to examine closely the concept of utility that emerges from van Praag's method of measurement, and to see if this concept is the appropriate one in the context of social welfare evaluation. My analysis raises some doubts in this regard. In brief, while I accept that van Praag's utility numbers do have the property of interpersonal comparability, I doubt if these numbers represent the concept of individual welfare that is relevant for building a social welfare function.
But first I want to make two preliminary remarks, to clear the way for subsequent discussion. First, by examining whether van Praag's utility numbers can serve as the basis for judging social well‐being, we are staying firmly within the ‘welfarist’ tradition, that is, the tradition in which individual utilities are seen to be the relevant informational basis for arriving at a judgement on social well‐being. As is well known, this tradition has recently come under severe attack from Rawls (1971), Sen (1987), and others who have exposed the inadequacy of utility as the basis of social welfare. Our intention here is not to defend the welfarist approach from these attacks, but merely to see whether within its own terms the welfarist approach can make good use of the van Praag utilities.
The second preliminary remark has to do with the cardinality of utility. Van Praag notes that the utility numbers yielded by his measurement method are essentially ordinal in nature, but towards the end of his paper he also proposes a specific method of arriving at cardinal utility. Is this cardinalization essential for the purpose of making social welfare judgements? Van Praag sometimes writes as if it is. For example, after noting that mainstream economics has for a long time accepted Robbins's denial of the existence of a measurable cardinal utility function, he explains its consequence thus: ‘Clearly this robbed any normative economics, which has to be based on the evaluation of individual situations and the evaluation of the state of the society as a whole by an aggregate of some sort of individual welfare evaluations, of any foundations.’ The suggestion here is that the absence of cardinality precludes the possibility of aggregating individual welfares into social welfare. Similarly, while referring to the practice of those economists who use a utility‐based social welfare function, he comments that their analyses are ‘either explicitly or implicitly based on a cardinal utility concept’, which ‘leads to a rather schizophrenic situation in economics as some authors, while on the one hand painstakingly ordinal, in normative studies accept cardinality in the way pictured above, if the need arises,’. Once again, cardinality is seen to be an essential attribute of utilities which enter into a social welfare function.
However, there is nothing essential about cardinality. In fact, it was not Robbins's denial of cardinality as such, but rather his denial of interpersonal comparability, that precluded the possibility of social aggregation. Also, the use of utility‐based social welfare functions by the ‘painstakingly ordinal’ economists does not necessarily imply their tacit acceptance of cardinality, though it does (p.388) imply their acceptance of interpersonal comparability. Indeed, it is the presence or absence of interpersonal comparability that is crucial. The absence of cardinality does not preclude comparability, nor does its presence ensure it—the two are entirely independent attributes. Recent advances in social choice theory have shown that, of the two, cardinality is not essential in the same way as interpersonal comparability is for permitting meaningful evaluation of social welfare. If utility is assumed to be cardinal but interpersonally non‐comparable, then it becomes impossible to evaluate social welfare in a way that will satisfy a set of very reasonable restrictions on the notion of social welfare. On the other hand, with ordinal but interpersonally comparable utilities there would typically exist some reasonable way of evaluating social welfare.1 Of course, certain methods of evaluation would be ruled out in the absence of cardinality—for example, the utilitarian principle—but other methods will remain open—for example, the Rawlsian leximin. We shall, therefore, leave aside the cardinalized version of van Praag's utility measure, take the measure in its original form, that is, the form of interpersonally comparable ordinal utility, and proceed to examine its usefulness for the purpose of evaluating social welfare.
We begin by asking the question: what do the van Praag utility numbers really mean? To answer this question, it will be helpful to see how van Praag deduces the various properties of his utility numbers. Two of these properties are of special interest in this context: the relativity and comparability of welfare. Relativity refers to the property that the welfare of an individual, to the extent that welfare can be derived from money, depends not on absolute income as is traditionally supposed but on relative income. Comparability refers to the property that the same utility number reflects the same level of welfare for everyone. These two properties are deduced empirically in the following manner.
Each individual is asked to attach certain income levels to a number of verbal labels such as ‘good’, ‘bad’, etc. Van Praag then converts these income levels into what he calls utility numbers by following a certain methodology. After studying the data across individuals certain regularities are observed. First, it is found that different people attach different income levels to the same verbal label. That is, what is a ‘good’ income for one person may not be ‘good’ for another. In general, the higher a person's current income the higher is his estimate of what a ‘good’ income is. From this it is deduced that welfare is a relative concept (hence the title of the paper). Second, it is observed that although different people attach different income levels to the same verbal label, when converted into utility numbers all these income levels are mapped into (almost) the same number. In other words, a given verbal label is transformed into the same utility number for everyone; there is a one‐to‐one correspondence between verbal labels and utility numbers, except for a small random variation. This means that if a certain utility number means ‘good’ for me it will also mean (p.389) ‘good’ for you. From this it is deduced that individual welfares are interpersonally comparable.
It is, however, important to note that behind these deductions there lies an implicit act of faith, without which neither the relativity nor the comparability of welfare can be established, despite the empirical evidence marshalled by van Praag. This act of faith consists in the untested assumption that the same verbal label implies the same level of welfare for everyone.
To see the role played by this assumption, take the relativity issue first. Van Praag often writes as if his empirical findings demonstrate the intrinsic relativity of individual welfare. But this is not quite so. What his empirical findings show is that the ‘good’ income for a rich man is higher than the ‘good’ income for a poor man. Evidently, the conception of ‘good’ is a relative one. In other words, the empirical evidence proves the relativity of verbal labels. To go on from here to claim that the conception of welfare is also relative, one must then assume that the same verbal label means the same level of welfare for everyone. In other words, one must assume a fixed correspondence between verbal labels and welfare levels so that the observed relativity of labels can be interpreted as relativity of welfare. Van Praag clearly makes this assumption, but it remains implicit.
The same assumption is also crucial for deducing the comparability of welfare. The claim that the utility numbers reflect interpersonally comparable welfare levels must be based on the demonstration that the same utility number stands for the same level of welfare for everyone. But van Praag's empirical evidence cannot, on its own, demonstrate this. The evidence merely shows that, given the methodology of converting incomes into utilities, the same utility number implies the same verbal label for everyone. In order to claim that the same utility number also reflects the same level of welfare for everyone, one must then bring in the assumption that a given verbal label stands for the same level of welfare for everyone—the same act of faith as before. To put it differently, the empirical evidence establishes a one‐to‐one correspondence between utility numbers and verbal labels, and the act of faith establishes a one‐to‐one correspondence between verbal labels and welfare; only by combining the two can one claim that there is a one‐to‐one correspondence between van Praag's utility numbers and individual welfare.
Thus both relativity and comparability of welfare, as deduced by van Praag, depends crucially on an act of faith and not on empirical evidence alone. There is nothing intrinsically wrong with that, for, as van Praag frequently points out, all science must start with some untested primitive concepts. The question is: how plausible is the primitive concept chosen, and are there any alternatives which may be no less plausible but which lead to very different interpretations of the same empirical phenomena?
The way van Praag justifies his particular primitive concept is to argue that the same ‘verbal label’ must mean the same thing to all people. Among other reasons, he mentions the socio‐cultural one that members of the same community (p.390) must have harmonized their linguistic conventions sufficiently well to mean roughly the same thing when they use a verbal label such as ‘good’. In particular, he suggests that the labels must have the same ‘emotional content’ for everyone. All this sounds plausible enough. But van Praag then takes a further step which is harder to justify. He takes it for granted that the same emotional content means the same level of welfare. It is this final step which enables him to equate verbal labels with welfare levels, and this equation in turn allows him to declare that welfare is relative and that his utility numbers reflect interpersonally comparable welfare levels. But there is no a priori reason why the emotional content of verbal labels should be seen in terms of levels of welfare. In other words, when you and I describe the respective income levels x and y as ‘good’, we may have the same emotional perception of these income levels, but the perception need not be that of equal welfare levels. Other interpretations are also possible. For example, x and y may yield different levels of welfare to you and me respectively, but y may give me the same welfare relative to what I consider to be the average norm, as x does to you relative to what you consider to be the average norm. In this interpretation, verbal labels do have the same emotional content, but this content now consists of ratios rather than levels of welfare.
I shall argue that this is not at all a fanciful interpretation. On the contrary, this will be seen to be the most natural interpretation of van Praag's findings, if we start from the conventional premiss that the level of welfare depends on the absolute level of income. Of course, this premiss contradicts van Praag's conception of the relativity of welfare; but, as we have seen, this property of relativity derives solely from the untested primitive concept that the same verbal label implies the same level of welfare. Since there is no a priori justification for accepting this, there is no compelling reason to accept the relativity property either. We are therefore entitled to substitute for van Praag's primitive concept the more conventional one that welfare depends on absolute income. And once we do that, the verbal labels as well as the utility numbers constructed by van Praag are seen to reflect ratios rather than levels of welfare.
To see how this happens, recall how the utility number is derived by van Praag. It is given by u i = (ln c i − μ)/σ, where c i is the income level attached to the ith verbal label, and μ and σ are respectively the mean and standard deviation of the logarithms of income levels attached by an individual to all the verbal labels. Van Praag has found that except for a random variation, the number u i attached to the ith verbal label is about the same for all individuals; this is the basis of his contention that the same utility number stands for the same verbal label. Now to see the relationship between u i and welfare, we make the simplifying assumption that σ is constant across individuals and then normalize it to unity.2 Also note that μ is really the logarithm of the geometric mean (m) of the incomes c i(i = 1, . . . , n) attached to n verbal labels. So the utility number u i can be seen (p.391) to be the proportionate difference between c i and m. Under the conventional premiss that welfare depends on absolute income van Praag's utility numbers can, therefore, be seen to represent the proportionate difference between the welfare derived from a given level of income and the welfare derived from some notion of average income. In other words, these utility numbers reflect some notion of relative welfare. Note that this is not the same thing as saying, as van Praag does, that welfare is relative. For him, welfare is an intrinsically relative concept (in the sense of being a function of relative income), and his utility numbers reflect the absolute levels of welfare thus conceived. What I am saying in contrast is that welfare is an absolute concept (in the sense of being a function of absolute income) and that van Praag's utility numbers reflect the ratios, and not the levels, of welfare thus conceived.
Now recall the empirically established correspondence between verbal labels and utility numbers, and add the just‐described correspondence between utility numbers and welfare ratios. The result is that the same verbal label will now be seen to stand for the same welfare ratio for everyone. Thus the general proposition that verbal labels have the same emotional content for everyone still remains valid, but that content now consists of ratios rather than levels of welfare. This argument illustrates the point made earlier that there is no a priori justification for interpreting the same emotional content of verbal labels as the same level of welfare. It is only by virtue of this interpretation that van Praag is able to claim that his utility numbers reflect interpersonally comparable welfare levels. If we reject his interpretation and start instead from the conventional premiss that welfare depends on absolute income, then the very same empirical findings imply that van Praag's utility numbers reflect interpersonally comparable welfare ratios.
This interpretation of utility numbers as ratios rather than levels of welfare creates obvious problems for social welfare evaluation. A welfarist social welfare function is typically constructed by aggregating the levels of individual welfare. If the van Praag utility numbers are seen to convey information about the ratios rather than levels of individual welfare, then clearly these numbers cannot be used as the building blocks of a social welfare function. This can only be done if we discard the conventional premiss that welfare depends on absolute income and embrace instead van Praag's own primitive concept, for in that case the utility numbers would indeed reflect levels of welfare. But since van Praag's primitive concept has no obvious superiority over the conventional one, doubts remain about the usefulness of his utility numbers as the foundation of social welfare evaluation. This is not to deny that his method of measuring the so‐called ‘utility’ numbers can none the less be very useful for many practical purposes, as has been amply demonstrated by many interesting applications of his method. What has been questioned here is its relevance for a utility‐based evaluation of social welfare.
Rawls, J. (1971). A Theory of Justice. Cambridge, Mass.: Harvard University Press.
Sen, A. K. (1970). Collective Choice and Social Welfare. San Francisco: Holden‐Day; republished, Amsterdam: North‐Holland, 1979.
—— (1987). On Ethics and Economics. Oxford: Basil Blackwell.
Helpful comments from Amartya Sen and Bernard van Praag are gratefully acknowledged without implicating either of them with the views expressed here.
(2) This assumption simplifies the intuitive exposition without detracting anything from van Praag's basic contentions regarding the relationship between utility numbers and verbal labels.