welfare, preference and freedom

Journal of Econometrics 50 (1991) 15-29. North-Holland

Welfare, preference and freedom*

Amartya Sen Harvard University, Cambridge, MA 02138, USA

This paper is concerned with the informational foundation of welfare-economic evaluation and the empirical bases of social welfare judgments. More particularly, it is concerned with the empirical implications of basing social evaluation on individual freedom, as opposed to individual welfare. This involves a substantial shift from the informational focus of standard welfare economics, with its dominant tradition of ‘welfarism’.

While the claims of individual preferences to be in the informational base of social welfare judgments are frequently seen as parasitic on welfarism, the claims relate more robustly to freedom-based social evaluation. In an axiomatic examination, it is argued that preference and freedom are very deeply interrelated, and that an affirmation of the intrinsic importance of freedom must inter alia assign fundamental importance to preference. This goes against some common presumptions about assessing freedom, and also against some axioms that have been proposed in the literature on ‘measuring freedom’.

1. Information, intrinsic importance, and instrumental role

I begin with some clarificatory remarks on methodological issues. The term ‘social welfare’, as standardly used in welfare economics, refers to the ‘ethical value’ or the ‘goodness’ of the state of affairs of the society. As used by the pioneers of modern welfare economics [Bergson (19381, Samuelson (19471, Arrow (195111, and following them in the literature gener- ally, ‘social welfare’ is simply the representation of the ‘goodness’ of the social state. The term leaves the determination of that value completely open and does not restrict the arguments or the functional forms of the ‘Bergson-Samuelson social welfare function’. In particular, despite the ‘welfarist’ sound of the term ‘social welfare’, the use of that concept does not

*For helpful discussions I am grateful to James Foster, Isaac Levi, Essie Maasoumi, Stephen Marglin, Siddiq Osmani, John Rawls, Thomas Scanlon, and Thomas Schelling. The research on which this paper is based was supported by the National Science Foundation.

0304-4076/91/$03.50 0 1991-Elsevier Science Publishers B.V. (North-Holland)

16 A. Sen, Welfare, preference, and freedom

presuppose a ‘utilitarian’ or ‘welfarist’ formulation of social objectives.’ This is important to note before proceeding with the analysis to be presented in this paper, which is concerned specifically with different informational bases for welfare-economic analysis, including nonwelfarist as well as welfarist and utilitarian structures.

A fundamental concept in this analysis is that of the ‘informational foundation’ of an evaluative system. In each evaluative structure, some types of factual matters are taken to be important in themselves, others not so. The former variables, which reflect the basic ends in that specific evaluative system, constitute the ‘informational basis’ of evaluative judgments in that system. The importance of these variables is intrinsic rather than derivative.

In contrast, the latter variables cannot sway such evaluations directly through intrinsic importance. In this sense, each evaluative system imposes - typically implicitly - certain ‘informational constraints’, which rule out classes of information from having a direct and first-hand role in evaluative judgments in that system. * In the axiomatic derivation of particular social welfare rules, the informational foundations can play an important - often decisive - function.3

For example, the informational foundation of utilitarian ethical calculus includes only unit-comparable individual cardinal utilities, and excludes all other variables. Consider the utilitarian maximand, the sum-total of individual utilities U, for all individuals i in the society:

Notice that if W is a complete representation of what is intrinsically valuable, then nothing other than these individual utilities {Ui:) have an uncondi- tional placing in this utilitarian evaluative system. In fact, aside from elimi- nating nonutility information from the informational foundation, eq. (1) also has the effect of excluding any direct role of the levels of individual utilities in ranking different states of affairs. This is because the ranking of any two

‘Welfarism is the demand that the evaluation of any social state be based exclusively on the utilities generated in that state. Utilitarianism can be factorized into welfarism (as defined above), sum-ranking (aggregating individual utilities by simply summing them), and consequen- rialism (judging the rightness of actions, policies, and other choices exclusively on the basis of the consequent states of affairs). The format of social welfare functions is not necessarily welfarist, though it is hard to dissociate it from consequentialism. On this and related matters, see Sen (1982a).

‘On the formal characterization and substantive role of informational bases in general and informational constraints in particular, see Sen (1970,1977,1986).

3See, for example, the axiom systems used in Sen (1970,1977,1986), Hammond (1976,1977), d’Aspremont and Gevers (1977), Maskin (1978,1979), Gevers (1979), Roberts (1980a, 1980b), Blackorby, Donaldson, and Weymark (19841, d’Aspremont (19853, among others.

A. Sen, Welfare, preference, and freedom 17

alternative states, say x and y, relates only to the utility difference that each person has between these two alternatives:

xRy- c[u,(x) -u,(y)] 20.

If, for example, we add a constant k to any person’s utility function U,, the social ranking of x and y will remain altogether unaffected, since the utifity differences will not be altered.4

One way of presenting a critique of utilitarianism is to argue in favour of the intrinsic importance of one or more of the excluded variables. Utilitarian judgments cannot be directly and constitutively affected by the variables not included in the informational foundation, and this ‘insensitivity’ can give grounds for criticism if it is decided that they should have such an influence.

However, being excluded from the informational foundation does not entail that the variable in question would have no effect on the evaluative judgments to be made. There can, obviously, be indirect effects through causal connections, and a variable can be instrumentally influential through its role in the determination of the intrinsically valuable variables. The accounting of indirect influences calls for causal analysis of instruments and their consequences.’

These are primarily empirical exercises. For example, if we are examining how income (seen only as an instrument) affects utility (taken to be intrinsically important), then the focus of the instrumental analysis must include the empirical relationship between income and utility (e.g., the characteristics of the individual utility functions). Such empirical investigations can form an important part of welfare-economic analysis, and applied econometric studies may, thus, be quite central in substantive welfare economics.6

2. Preference, welfare, and freedom

In the standard welfare-economic literature, individual preferences are given a substantial - sometimes exclusive - role in the informational founda-

4There are some complex technical issues here, on which - and on related matters - see Sen (1970, 1977), d’Aspremont and Gevers (1977), Hammond (19771, Maskin (1978), Gevers (1979), Roberts (1980a, 198Ob), Blackorby, Donaldson, and Weymark (1984), d’Aspremont (1985), among others.

51n the recent literature on ‘multidimensional’ social welfare or inequality [see Kolm (1977), Atkinson and Bourguignon (19821, Maasoumi (1986,1989), among others], the ‘dimensions’ have tended to include variables with an instrumental role, in addition to variables of intrinsic importance.

‘Examples of extensive use of applied economics and econometrics for welfare-economic analysis can be found in such works as Atkinson (1975,1989), Jorgenson, Lau, and Stoker (1980), and Jorgenson and Slesnick (1984a, 1984b).


tion of ‘social welfare functions’. Much of traditional welfare economics is ‘welfarist’ in the sense that the goodness W(x) of any social state x (sometimes called the ‘social welfare’ of x) is taken to depend, ultimately, only on the individual utilities or welfares (W&X)) of the people in that state.’ There is also a long tradition in mainstream economics of identifying individual utility or welfare y. with the fulfillment of individual preferences Ri.8 The two together make individual preferences between any social state and another, ultimately, the only basis of socially ranking those two states.’ Traditional welfare economics [e.g., Edgeworth (18811, Pigou (1920), Ramsey (192811 has tended to give this role to individual preferences, and this has been reinforced by the reformulations brought about by Bergson (1938), Samuelson (19471, and Arrow (1951).”

Recently, there have been several attempts to give a more central and constitutive place to the freedoms and liberties of individuals in the determination of social welfare. ” The freedoms in question can take a negative form (e.g., freedom from interference and hindrance), or a positive character (e.g., freedom to do this or be that). I2 Basing the evaluation of social welfare on individual freedoms involves a rejection of ‘welfarism’, which demands that social welfare must be a function only of individual welfares. It is tempting to think of freedom-based approaches as being hostile to preference-based social judgments. I shall argue against that conclusion in the next two sections of this paper. This will involve the rejection of two common presumptions in welfare economics, viz: (1) identifying preference fulfillment with individual welfare and (2) dissociating freedom from preference fulfilment. I shall dispute both these beliefs.

‘On the rationale of the welfarist approach, see Edgeworth (1880, Pigou (1920), Samuelson (1947), Arrow (1950, Harsanyi (1955), Hare (1980, Mirrlees (1982), among others.

son different aspects of the links between them, see Hicks (1939), Samuelson (1938), Little (1950), among others.

‘This result can also be obtained indirectly through other sets of axioms (e.g., the combination of unrestricted domain, independence of irrelevant alternatives and the weak Pareto principle imposed on an Arrovian social welfare function). On this question, see Arrow (1951,1977), Sen (1970,1977), d’Aspremont and Gevers (19771, Gevers (1979), d’Aspremont (1985), Blackorby, Donaldson, and Weymark (1986), among others. On related matters, see Kemp and Ng (1976) and Pollak (1979).

‘“There is, however, some ambiguity in the uses of the term utility, in particular regarding its connections with well-being, preference, and choice.

“As was mentioned earlier, the inclusion of freedom or liberty as determinants of social welfare places the importance of these variables within a consequentialis? evaluative structure. Those who accommodate liberty or freedom in nonconsequentialist, deontological forms, seek different routes; see, for example Nozick (19741, Gardenfors (1981), Sugden (1981), Gaertner, Pattanaik, and Suzumura (1989). Buchanan’s (1975,1986) justly influential analysis includes both deontological and consequentialist features.

r21 have tried to discuss the relevance of both types of freedoms in Sen (1970,1982b, 1985a). The literature on libertarian valuations in social choice theory is now quite extensive; for helpful critical evaluations and comparisons, see Suzumura (19831, Wriglesworth (1985), Riley (1987,1989), Gaertner, Pattanaik, and Suzumura (19881, Deb (1989), Hamlin (1989).


3. Nonwelfarist relevance of preference

There is some ambiguity regarding what preference is supposed to stand for and how it is linked with welfare or utility. If preference is simply defined as the pursuit of welfare, or if utility is seen as just the real-valued representation of preference, then there is clearly no big gap between basing social judgments of states on individual utilities or welfares, on the one hand, and basing them on individual preferences, on the other.

While the term preference is ambiguous, one of its commonly attributed meanings links it inseparably with choice.13 Indeed preference is often seen as nothing other than the binary relation underlying a choice function (assuming that the choice function satisfies binariness).14 If preference is defined in terms of individual choices as such, then its identification with individual welfare involves a substantive empirical theory, since the two are not then analytically linked. That identification can be disputed on various grounds (such as the existence of reasons for preference other than direct or indirect pursuit of individual welfare). l5 If preference is divergent from

individual welfare or utility, then welfarism would not demand that social welfare judgments be based on individual preferences - indeed it would then reject the preference-based procedure. In the welfarist approach - dominant in traditional welfare economics - the case for basing the social evaluation of states on individual preferences turns on the correctness or falsity of the identification of preference with welfare or utility.

It is, however, arguable that preferences - in the sense of reflecting individual choices - may be directly relevant for social judgments of states of affairs, since the goodness of states cannot be evaluated without regard to what people would themselves like to choose - no mutter what motivates them towards that choice. This presumption is certainly among the basic beliefs underlying the origin of normative social choice theory, beginning with the pioneering work of Arrow (1951).16 If the preferred choices of the members of the society were taken as constituting the appropriate informational basis of social evaluation of states, then the truth or falsity of the

13This is the case in Arrow’s (1951) formalization of the social choice problem (see particularly ch. 2).

140n the conditions needed for binariness of choice, see Sen (1971), Fishburn (1973), Herzberger (1973), Suzumura (1983), among others.

150n this see Sen (1973,1982a), Scitovsky (19761, Hirschman (1982,1984), among other contributions.

16Arrow, in fact, insisted further that the arguments of the social welfare function must not go beyond individual ordinal, noncomparable preferences representing their choices: ‘We will therefore assume throughout this book that the behavior of an individual is describable by means of a preference scale without any cardinal significance, either individual, or interpersonal’ [Arrow (1951, p. 101. On the other hand, those preferences need not be based only on individual tastes regarding their own consumption, or only on concern for their own welfare. ‘The individual orderings which enter as arguments into the social welfare function as defined here refer to the values of individuals rather than to their tastes’ (p. 23).


congruence of individual preference and individual welfare will not affect the status of preference in directly influencing social welfare. On the contrary, it would only determine what relevance individual weZfure might have in social evaluation.

This seemingly simple ‘twist’ in the characterization of the informational foundation of social welfare judgments can have profound effects on the nature and interpretation of empirical investigations related to welfare-economic judgments. By seeing individual preference as intrinsically important and individual welfare only derivatively so, the empirical studies have to concentrate primarily on choice as such. There will, of course, be grounds here too for ‘correcting’ observed choices to obtain considered preferences, and attention has to be paid to the possibility that ignorance, hastiness, or for that matter, strategic considerations, may distort actual choices vis-a-vis what would be chosen with informed reflection without strategic deflections. But, in this approach, the ‘corrections’ have to be neutral between the different motivations that can influence choice. In particular, there will be no ground for a ‘welfarist’ bias in interpreting and doctoring observed choices in the direction of individual welfare.”

This will differ not only from the nature of the empirical exercises of the kind that Pigou (1920) and other welfarists have seen as central to welfare economics, it could even go against the basic Benthamite strategy, as Arrow (19.51) puts it, ‘to ground the social good on the good of the individuals’ (p. 22). If individual preferences (and choices based on them) are not geared to the pursuit of the good of the respective persons (but, partly or wholly, to other objectives and values), that - in this reformulated framework - is not a source of any embarrassment in taking preferences as constitutive of the informational base of social evaluation. If individual preference is what counts, then the role of ‘the good of the individual’ has to be derivative, unless, of course, the good of the individual is simply defined as the fulfilment of what the individual prefers (no matter what his or her motives may be).

4. Freedom and preference: Axioms and measures

Various axioms for set comparison for ‘measuring freedom’ have been proposed and analysed in the literature. l8 There are also other axiomatiza- tions of set comparison with motivations different from that of evaluating

“In terms of the distinction between the ‘well-being aspect’ and the ‘agency aspect’ of a person [on which see Sen (1985a)], this relates the importance of individual preference to the latter, irrespective of its connection with the former.

“See Sen (1985b, 1990a, 199Ob), Suppes (1987), Pattanaik and Xu (1990).


freedom. The axioms to be used have to be seen in the light of the specific

purpose. Set comparison for evaluating freedoms in general differs substantially in

motivation from set comparison for utility maximization in the future when future tastes are unknown. The latter exercise has been interpreted as one of ‘preference for flexibility’ [e.g., Koopmans (19641, Kreps (197911, and its axiom structure has been geared entirely to utility maximization with uncer- tain future tastes, rather than to valuing freedoms - present or future - with known preferences. l9 In what follows, preferences are taken to be known

with certainty. The literature on set comparison for decisions under uncertainty ” is also

of indirect interest in the present context, though the motivation there is again quite different, calling for a dissimilar axiomatic system. For example, the addition of an inferior alternative does make the set worse in the case of uncertainty (since the substandard alternative may well ultimately emerge no matter what the person himself wants), but when the person has the freedom to choose any alternative from the given set, the addition of an inferior alternative need not make the situation worse for him (since he can simply reject the substandard alternative). Again, I shall assume no uncertainty.

In the proposed axiom structures for set comparison both for ‘preference for flexibility’ (Koopmans-Kreps) and ‘decision under uncertainty’ (Kannia- Peleg), the role of preferences in the axiom systems is obvious enough. It may, however, be tempting to think that preference as such need not have that role for ‘measuring freedom’, without uncertainty. As was mentioned earlier, preference and freedom are frequently contrasted with each other in terms of their respective contents and demands. The contrast is not hard to understand in an elementary form. Freedom would seem to be primarily related to the specification of the set from which one can choose, whereas preference is mainly a matter of the element one would choose from each given set. It is not unreasonable to argue that if a person has an enlarged set to choose from, then his freedom, in some sense, must be at least as large, if not larger, no matter what his preferences are and what he actually chooses from the respective sets. It is also easy to consider a scenario in which a person’s freedom expands even though the person ends up in a less preferred state.

However, this type of simple contrasting between freedom and preference can be deeply deceptive. If freedoms are to be compared, the sets from which choices have to be made (let us call them ‘menus’> have to be weighed

“On the motivational distinctions, see Sen (1985b, pp. 60-67).

“See, for example, Kannai and Peleg (1984), Fishburn (1984), Heiner and Packard (19841, Barbera and Pattanaik (19841, Holzman (19841, Barbera, Barrett, and Pattanaik (1984), Pattanaik and Peleg (1984), Nitzan and Pattanaik (1984).


against each other in a systematic way - not merely in the simple case in which one set is a subset of another. 21 Can that extensive exercise of set comparison - reflecting freedom - be independent of the preference ordering over the elements of the respective sets? It is hard to see how this can be the case, in general. The evaluation of the freedom I enjoy from a certain menu must depend to a crucial extent on how I value the elements included in that menu. Any plausible axiomatic structure in the comparison of the extent of freedom would have to take some note of the person’s preferences.

The nature of the problem can be brought out by considering a collection of possible axioms in comparing the extent of freedom. Let X be the universal set of alternative social states, with typical elements x, y, z, etc. We take X to be finite, though this assumption is not necessary for establishing the main contentions to be presented here. Let Y be the power set of X, that is the set of all nonempty subsets of X, which can be denoted 2” - @. The elements of Y (i.e., the subsets of X> are A, B,C, etc. The person whose freedom is being judged has a considered preference ordering R over the set of social states X.22 We follow the convention of R standing for ‘weak preference’ (preferred than or indifferent to), P for ‘strict preference’ (strictly preferred than), and I for ‘indifference’. The relations R*, P*, and I*, defined over Y, respectively represent the relations ‘offers at least as much freedom’, ‘offersstrictly more freedom’, and ‘offers exactly as much freedom’. Let #S stand for the cardinality of set S (i.e., the number of elements of SI. Also, 2 and 3 denote weak set inclusion and strict (asymmetric) set inclusion. As was mentioned earlier, no uncertainty is admitted.

We also define ‘preference dominance’ relations over subsets of X, with D” and Ds standing, respectively, for weak and strong dominance.

Weak preference dominance : AD” B if and only if there is a subset A’ of A such that #A’ = #B, and if further there is a one-to-one correspondence k(e) between A’ and B such that for all x in A’, we have xRk(x).

Strict preference dominance : AD” B if and only if AD” B holds, and further, for all x in A’, we have xPk(x).

Now consider examples of three classes of axioms for the comparison of freedoms. There are preference-based axioms (denote them axioms of type A), preference-independent axioms (axioms of type B), and some constructive

“There is a complication even when this subset condition is fully satisfied, on which more presently.

**We dispense with the subscript i in R,, reflecting personal indexing, since we are considering only one individual in the present context.


axioms relating freedom judgments in some cases to freedom judgments in other - related - cases, in the absence of uncertainty (axioms of type C).23

Axiom A.1 (weak preference dominance): AD” B =$ AR* B.

Axiom A.2 (strong preference dominance): Axiom A.1 holds, and furthermore AD” B *AP*B.

Axiom B.1 (weak set dominance): A ZB *AR*B.

Axiom B.2 (strong set dominance): Axiom B.l holds, and furthermore AIBAAP*B.

Axiom B.3 (weak cardinal@ ranking): #A 2 #B *AR*B.

Axiom B.4 (strong cardinality ranking): Axiom B.3 holds, and furthermore #A>#B-AP*B.

Axiom C. 1 (identical expansion): If x belongs neither to A nor to B. then:

AR*B*(Au{x})R*(Bu{x)).

Axiom C.2 (weak composition): If A n C = B fl D = @, then:

[AR*B&CR*D]* [(AuC)R*(BuD)].

Some interrelations within the same category are patently clear. It is definitionally obvious that: A.2 entails A.l, B.2 entails B.l, and B.4 entails B.3. It is also fairly obvious that B.3 entails B.l and that B.4 entails B.2.

Turning now to intercategory connections, it is easy to see that:

(T.l) A.1 entails B.l and B.3 entails A.l.

While A axioms and B axioms are differently based, respectively on preferences and set inclusions, the definition of preference dominance in A.1 covers set inclusion as a special case. In order to declare AR*B, axiom A.1 demands that A be at least as large a set as B (in terms of cardinality),24 and

23Axioms A.1 and A.2 were proposed in Sen (1985b). For motivational discussions regarding the other axioms (not all consistent with each other), see Sen (1985b, 1990b), Suppes (19871, Pattanaik and Xu (1990).

24Note that an instrumental view of freedom (i.e., valuing freedom only for the value of the outcome it permits to achieve) can dispense with this requirement on set size in the preference- based axiom A.l. For example, if x is strictly preferred to, say, y and z, then from that instrumental perspective the unit set (x) is as good as the set (x, y, z). But if freedom of choosing has some intrinsic value as well, then it is possible to argue that {n) can give less freedom than {x, y, z). On this and related matters, see Sen (1985b, ch. 7).


that for some subset A’ of A, of the same size as B, there is element-by-element weak dominance of A’ over B in terms of preference. The first part of that requirement about the size of sets connects B.l to A.l. Further, if sets can be evaluated by their respective cardinality (as in B.31, then the antecedent condition in A.1 will automatically yield the specified ranking of freedom. The converse does not, of course, hold, since A.1 does have a preference-based requirement not contained in the antecedent of B.3.

More interestingly there are also possibilities of contradiction between the two types of axioms. Perhaps the simplest way of bringing this out is to consider the ordering of unit sets, such as {x}, {y), etc. Take two alternative axioms dealing with this subset Y* of Y.

Axiom A*: For all x, y in X: if xPy, then (x}P*{y).

Axiom B*: For all x, y in X: (x)Z*(yl.

Axiom B*, which is part of the axiom structure proposed by Pattanaik and Xu (19891, goes entirely by the cardinal&y of the set only, in the special case of unit sets, whereas axiom A* is based on preference. The conflict between the two brings out the clash of the two approaches in a simple - but important - case, viz., that of unit sets.

The following results are easy to show.

(T.2.1) Axiom A.2 entails axiom A*.

(T.2.2) Axiom B.3 entails axiom B*.

(T.2.3) Axioms A.2 and B.3 are inconsistent.

The first two results are easily established, and (T.2.3) is a deduction from the fact that A.2 and B.3 have mutually contradictory entailments, as given by (T.2.1) and (T.2.2).

Note also that axioms B.l and B.2 do not provide any nontrivial ranking of distinct unit sets (whereas axioms B.3 and B.4 both entail axiom B*). In fact, since axioms B.l and B.2 stick to set inclusion only (rather than cardinality of the sets), they yield very incomplete orders. 25 The interesting contrasts lie between A.1 and A.2, on the one hand, and B.3 and B.4, on the other, and they in turn take us respectively to axioms A* and B*.

In comparing axioms A* and B*, it is fair to say that many people’s intuitions tend to work in favour of B*, and this would seem to go against the

=Axiom B.l is very unassertive, but B.2 is less so. For example, if a set is enlarged by including an alternative which no one would choose in relevant circumstances (e.g., being beheaded at dawn), the addition of that alternative may not necessarily be seen as a strict enhancement of freedom, contradicting B.2.


preference-based view of freedom. The argument goes something like this. Neither 1x1 nor {y} offers any freedom at all, since they are unit sets. So they must have the same extent of freedom (to wit, nil).

What this line of reasoning overlooks is the fact - central to preference- based reasoning - that in judging whether we have ‘the freedom to lead the life we would choose to lead’, we have to bring in counterfuctual choices (what I would have chosen). To illustrate, suppose you decide to read a particular book, say Cymbeline, one Sunday; you could have chosen any book you had, but you chose Cymbeline. Consider now an alternative scenario in which you are forced to read another book, say, about the reminiscences of a matinee idol, which you would not have chosen to read. Consider a third scenario in which you are given no choice and simply ordered to read Cymbeline, which you would have chosen to read anyway. There is no question that in the last two scenarios, your freedom is reduced. But it would be absurd to say that you are equally unfree in the two last cases. In the second case, viz., reading the reminiscences of the matinee idol, you are being obliged to read a book you would not have chosen at all, whereas in the third case, viz., reading Cymbeline, you are being obliged to read the book you would have chosen to read anyway. You do not have the freedom to choose between the two books (something obviously is lost here), but you do have the freedom to read the book you would have, in any case, chosen to read. This would suggest that axiom A* has some merit, viz. that of discrimination between preferred and unpreferred alternatives, and this sense of discrimination axiom B* does not have.

Note that this conclusion does not imply that nothing is lost by your losing the freedom to choose x or y, and being obliged to choose what you would have chosen anyway. The no-loss view may be an appropriate judgment for comparison of consequences (narrowly defined), but in terms of comparison of freedom, it is reasonable to argue that, given xPy, the ordering of freedom should be: IX, y}Z?{x)P( ~1.‘~

In the real world, the contrast between axioms A* and B* can be quite important.27 Given the way modern society is organized, many decisions have to be taken at a public - rather than personal - level. For example, public policy may eliminate smallpox, but does not give us the option of (1) having smallpox {yl or (2) not having smallpox (xl. It is absurd to say that we have us much unfre&om if we are forced to live in a world in which we cannot have smallpox, as in a world in which we cannot escape it. We do have more ‘freedom to live as we would like’, if smallpox is eliminated, since we would choose not to have it if we do have that choice. This is in line with axiom A*

Z6The first R can also be made into a strict P without contradicting the preference view of freedom.

*‘This and related issues are discussed in Sen (1982c, 1990b).


rather than B*, and illustrates the abiding relevance of preference for the evaluation of freedom.

It is also interesting that even the defenders of axiom B* typically do not defend the more demanding axiom B.3. 28 That axiom will require that we ignore the nature of the alternatives in the menu and simply count their numbers in general to assess freedom. The choice among ‘a nasty life’, ‘a terrible life’, and ‘an unspeakable life’ gives us, according to axiom B.3 (and of course B.4), just as much freedom as the choice between ‘a fine life’, ‘an excellent life’, and ‘a wonderful life’, simply because each set has three elements. This part of axiom B.3 may be called B.3.1.

Axiom B.3.1 (cardinality-based indifference): #A = #B 2 A I *B.

But there is problem for those who find B.3.1 unacceptable but would defend the less demanding axiom B*.

(T.3) Given axiom C.2, axioms B* entails B.3.1.

This is easily established. Take A and B with the same cardinality. Partition each into unit sets - each will have the same number of unit sets. Take any one-to-one correspondence between the two classes of unit sets, and note the indifference relation I* between each such pair of sets (given axiom B*). Then put them together one by one to get back to sets A and B. Due to repeated use of the characteristic of composition (axiom C.21, we shall have: AI*B.

5. Concluding remarks

I shall not try to summarize the paper, but will make a few concluding observations.

First, in relating empirical work to welfare-economic evaluation, it is useful to pay particular attention to the informational bases of evaluative judgments that provide the foundations of welfare-economic analysis. Empirical works in applied economics and econometrics can relate closely to the characterization of informational bases and the instrumental connections linking other variables to those included in the informational foundation of ethical judgments (section 1).

Second, this paper has been particularly concerned with the role of preference in welfare-economic analysis (sections 2-4). Even though the concern with individual preference is typically justified in standard welfare

28Pattanaik and Xu (1990) are, however, led to some qualified support for B.3 and B.4, as a consequence of the other axioms they use, including B*.


economics in terms of a ‘welfarist’ framework of analysis, the relevance of preference is, in fact, much deeper than that (section 3).

Third, if the informational foundation of welfarism is replaced by that of individual freedom as constitutive of a good social state, the need to use empirical information on individual preferences remains at least as strong. Indeed, it can be argued that welfarism provides no guarantee of the constitutive importance of individual preference (section 31, whereas freedom-based social evaluation does provide such a guarantee (section 4).

Finally, comparisons of freedoms that a person has involve a complex set of considerations, but the need to base such comparisons on information regarding individual preference is inescapable. Attempts to bypass preference-type information (as in axioms of the B category) in judging the extent of freedom are deeply problematic (section 4). The problem extends even to judgments of unit sets, e.g., axiom B*. The need to include preference information in judging freedom has some serious implications for the direction of empirical research in evaluating individual freedom. And that in turn is of obvious relevance for welfare-economic analysis based on the informational foundation of freedoms rather than of welfares.

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