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On Economic Inequality$

Amartya Sen

Print publication date: 1973

Print ISBN-13: 9780198281931

Published to British Academy Scholarship Online: November 2003

DOI: 10.1093/0198281935.001.0001

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A.7.3 On Weights and Valuations

A.7.3 On Weights and Valuations

On Economic Inequality
Oxford University Press

Since functionings are robustly heterogeneous, the need to weigh them against one another arises under all approaches geared to functionings, whether the concentration is on realized functioning vectors x (as with the choice application), or on the capability sets K (as with the options application). The latter has the further task of comparing sets rather than points in this space, and involves the additional issue that the importance of freedom can stretch well beyond the value of the particular element that is chosen (except in the special case of elementary evaluation). But no matter whether we stop with valuing functioning vectors (as under the choice application), or go beyond it (as required by the options application), we have to value the functioning vectors in the first place. The (p.204) weighting of different functionings vis‐à‐vis each other is, thus, central to the capability approach.

This weighting requirement is often seen as a ‘difficulty’ with the capability approach. It is not, however, a special problem that arises only with this approach, since heterogeneity of factors that influence individual advantage is a pervasive feature of actual evaluation. While we can decide to close our eyes to this issue by simply assuming that there is something homogeneous called ‘the income’ in terms of which everyone's overall advantage can be judged and interpersonally compared (and that variations of needs, personal circumstances, prices, etc., can be, correspondingly, assumed away), this does not resolve the problem—only evades it. Real‐income comparison involves aggregation over different commodities, and in judging comparative individual advantages, there is the further problem of interpersonal comparisons taking note of variations of individual conditions and circumstances.

In more fully worked‐out theories, considerable heterogeneity is explicitly admitted. In Rawlsian analysis, primary goods are taken to be constitutively diverse (including ‘rights, liberties, and opportunities, income and wealth, and the social bases of self‐respect’), and Rawls (1971) proposes to deal with them through an overall ‘index’ of primary goods holdings.142 Turning to utilities, while many utilitarians tend to assume that utility is homogeneous, the need to see it as having diverse contents—even for a given person—has been well discussed by Aristotle, John Stuart Mill, and many others.143 It is only through arbitrary exclusion that the issue of heterogeneity (p.205) geneity can be avoided in the evaluation and comparison of individual advantages or welfares.

The problem is not, however, one of ‘all or nothing’. When some functionings are selected as significant, an evaluative space is specified, and this itself leads to a ‘partial ordering’ over the alternative states of affairs. If an individual i has more of a significant functioning than person j, and at least as much of all such functionings, then person i clearly has a higher‐valued functioning vector than j has. This partial ordering can be ‘extended’ by further specifying the possible weights. A unique set of weights will be sufficient to generate a complete order, but it is typically not necessary. With any given ‘range’ of weights (i.e., the weights being confined to a specified range), there will be a partial ordering, and this will get systematically extended as the range is made more and more narrow. Somewhere on the way—possibly well before the weights are unique—the ordering will become complete.144 But even with an incomplete ordering many decision problems can be adequately resolved, and even those that are not fully resolved, can be substantially simplified (through the rejection of unambiguously lower‐valued alternatives).

How are the weights to be selected? This is a judgemental exercise, and it can be resolved only through reasoned evaluation. In making personal judgements, the selection of the weights will be done by a person in the way she thinks is reasonable.145 But in arriving at an ‘agreed’ range for social (p.206) evaluation (e.g., in social studies of poverty), there has to be some kind of a reasoned ‘consensus’ on weights (even if it is of an informal kind). While the possibility of arriving at a unique set of weights is rather unlikely, that uniqueness is not really necessary to make agreed judgements in many situations, and may not indeed be required even for arriving at a fully complete ordering.146

This way of looking at the problem raises two different types of issues. First, would the use of such weights—or ranges of weights—be necessarily arbitrary and baseless, in contrast with, say, utilizing already available weights in the form of market valuation, which can be reflected in real income comparisons? Second, can we really do any inequality analysis with ordinal comparisons only (if that is the form that capability comparisons take)?

The former issue is taken up first; the latter is postponed until section A.7.5. In the democratic context, values are given a foundation through their relation to informed judgements by the people involved. The discipline of such valuation has been extensively explored in the contemporary literature on social choice theory as well as public choice theory. While they differ somewhat in their approach, there is, as discussed in Sen (1995), much complementarity between them, and a more complete characterization of basing social judgements on public acceptance can be obtained by combining the two disciplines. It is not so much a question of holding a referendum on the values to be used, but the need to make sure that the weights—or ranges of weights—used remain open to criticism and chastisement, and nevertheless enjoy reasonable public acceptance. Openness to critical scrutiny, combined with—explicit or tacit—public consent, is a central requirement of non‐arbitrariness of valuation in a democratic society.147 The (p.207) non‐uniqueness of weights it may yield is part of the discipline of evaluation (as has been discussed already). The exercise is not basically different from what is needed for the setting of a ‘poverty line’, or the evaluation of an ‘environmentally adjusted national income’, or the use of an ‘inequality index’ in national statistics (like Atkinson's measure for a chosen α).

In this context, Robert Sugden has raised the important question as to whether the capability framework, which requires evaluative weights to be devised, is really ‘operational’ (Sugden 1993, p. 1953). T. N. Srinivasan (1994) has promptly answered the question in the negative, pointing out that the ‘argument that varying importance of different capabilities in the capability framework is analogous to the varying value of different commodities in the real‐income framework is not an adequate response’ (p. 239). In defending this claim, Srinivasan quotes Sugden to the effect that ‘the real‐income framework includes an operational metric for weighting commodities—the metric of exchange value’.148 How much of an argument is this for sticking to the commodity space and market valuation in making comparative judgements on personal advantages, rather than using information on functionings and other features of quality of life and individual advantage?

Certainly, market prices exist for commodities, and do not for functionings. But how can evaluatively significant weights—whether of commodities or of functionings—be simply ‘read off’ from some other exercise (in this case, of commodity exchange), without addressing the issue of values in this exercise (the comparison of individual advantages)? There are two distinct issues here of practical importance. The first, and perhaps less basic, is that the problems of externalities, inequalities, and other concerns may suggest that market prices be ‘adjusted’. We have to decide whether such adjustments should be made, and if so, how this should be done, and in the process an evaluative exercise cannot really be avoided. (p.208) For example, equating the millionaire's dollar to that of the pauper involves a procedure of comparison that is certainly open to evaluative questioning, even if that questioning is not encouraged.

The second—and the more fundamental—problem is that ‘the metric of exchange value’ (recommended by Srinivasan), though operational in its own context, was not devised to give us—and indeed cannot give us—interpersonal comparisons of welfare or advantage. Some confounding has occurred on this subject because of misreading the tradition—sensible within its context—of taking utility to be simply the numerical representation of a person's choice. That is a useful way of defining utility for the analysis of consumption behaviour of each person taken separately, but it does not, on its own, offer any procedure whatever for substantive interpersonal comparison. Samuelson's (1947) elementary point that ‘it was not necessary to make interpersonal comparisons of utility in describing exchange’ (p. 205) is the other side of the same coin: nothing about interpersonal comparison of utility is learnt from observing exchange or ‘the metric of exchange value’.

To take the consumption of the same value of commodities by two persons as entailing the same utility for each involves a big jump in the reasoning. Sometimes the assumption is made that if two persons are observed to have the same demand function, then they must have the same level of interpersonally comparable utility for any given commodity bundle. But this too is a non sequitur.149 If instead of assuming that each person gets the same utility as others do from the same commodity bundle, we had assumed that one gets exactly half the utility that another gets from each respective bundle, that too would be perfectly consistent with all the behavioural observations (including the shared demand function).

This is not merely a ‘finicky’ difficulty of theoretical interest; it can make a very big difference in practice as well. For (p.209) example, even if a person who is disabled or ill or depressed happens to have the same demand function as another who is not disadvantaged in this way, it would be quite absurd to assume that she is having exactly the same utility or well‐being from a given commodity bundle as the other can get from it.

At the practical level, perhaps the biggest difficulty in basing interpersonal comparisons of advantage on real‐income comparisons lies in the diversity of human beings. Differences in age, gender, special talents, disability, proneness to illness, etc., can make two different persons have quite divergent substantive opportunities even when they have the very same commodity bundle. When we have to go beyond simply observing market choices, which tell us little about interpersonal comparisons, we have to use additional information, rather than simply the good old ‘metric of exchange value’.

The evident fact that market‐price‐based evaluation of advantage or well‐being or utility from commodity bundles gives the misleading impression—at least to some—that an already available ‘operational metric’ has been pre‐selected for evaluative use is itself a limitation rather than an asset. For informed scrutiny by the public, the implicit values have to be made more explicit, rather than being shielded from scrutiny on the false ground that they are part of an ‘already available’ evaluative metric. There is a real need for openness to critical discussion of evaluative weights, and it is a need that applies to all procedures for devising such weights. It is not a special problem for assessing functionings or capabilities only.


(142) Drawing on Arrow's (1951) impossibility theorem and its single‐profile extensions, various ‘impossibility theorems’ have been presented about the existence of satisfactory overall indices of Rawlsian primary goods (see Plott 1978, Gibbard 1979, Blair 1988). As in the case of Arrow's Theorem and its variants, informational limitations play a crucial part in precipitating these impossibility results. The case against imposing such informational limitations is discussed in Sen (1991b).

(143) Interpersonal comparison of utilities raises other problems of diversity (viz. personal variations), which have been much discussed in the literature since Robbins's (1932, 1938) classic critiques (arguing that ‘no common denominator of feelings is possible’).

(144) The formal relations between systematic narrowing of the range of weights, and monotonic extending of the generated orderings, have been explored in Sen (1970a, 1970b, 1982a), Blackorby (1975), Fine (1975), Basu (1980). The use of the ‘intersection approach’ in OEI‐1973 (pp. 72–5) relates directly to this procedure. See also the use of intersection quasi‐orderings in the earlier sections of this annexe. The approach of intersection quasi‐orderings can be combined together with ‘fuzzy’ representation of valuation as well as measurement of functionings, on which see Casini and Bernetti (1996) and also Chiappero Martinetti (1994, 1996).

(145) The central issue is the need to judge and evaluate—an exercise in reasoning, which is not the same thing as the feelings (such as pleasures and desires) on which classical utilitarianism concentrates. On the need for—and standards of—reasoning in evaluative exercises, see Rawls (1971, 1993), Scanlon (1982), Williams (1985), Nagel (1986), Nozick (1989), among other contributions. In some modern versions of utilitarianism, the role of reasoning is stressed in the characterization of utility itself, thereby reducing the gap between the two perspectives; see Hare (1981) and Griffin (1986).

(146) See Chs. 7 and 7* in Sen (1970a).

(147) Some of the most insightful observations on this subject can be found in Frank Knight (1947).

(148) In fact, Sugden had gone on to say that it ‘remains to be seen whether analogous metrics can be developed for the capability approach’, taking a position rather less ‘closed’ than Srinivasan's.

(149) Explanations on why this is an error have been repeated persistently; see Samuelson (1947), Graaff (1957, pp. 157–8), Gintis (1969), Fisher and Shell (1972, p. 3), Fisher (1987, 1990). Evidently, this has not prevented its recurrence.