On Sen s Liberal Paradox and its Reception within Political Theory and Welfare Economics

On Sen s Liberal Paradox and its Reception within Political Theory and Welfare Economics Pieter Vanhuysse 1 Politics (2000) 20(1) pp. 25 31 In this article, Amartya Sen s seminal proof of the impossibility of a Paretian liberal is briefly reviewed. I then discuss the reception of this alleged liberal paradox within the fields of political theory and welfare economics. In particular, I examine the criticisms made by Brian Barry, and their wider implications for the field of social choice theory. It is argued that the various criticisms made on Sen s characterisation of liberty are fundamental, and that Sen s subsequent defence of his position is unconvincing. Moreover, there remain some wider doubts as to the usefulness of social choice theory s SWF approach to individual rights and freedoms. Sen s liberal paradox In his seminal 1970 paper The Impossibility of a Paretian Liberal, the 1998 Economics Nobel Prize laureate Amartya Sen (1982a, pp. 287 288) proved that there is no social decision function that can simultaneously satisfy the following three conditions: 1. U (Unrestricted domain): every logically possible set of individual preferences is included in the domain of the social decision function; 2. P (Pareto optimality): if every individual prefers any alternative x to another alternative y, then society must prefer x to y. 3. L (which Sen called Liberalism ): for every individual i, there is at least one pair of alternatives, say (x,y), such that if this individual prefers y to x, then society should prefer y to x. Sen illustrated this impossibility result with the example of two individuals, A (the Prude), and B (the Lewd), having the following preferences concerning the reading (a, resp. b) or non-reading (Na, resp. Nb) of D.H. Lawrence s allegedly spicy book, Lady Chatterley s Lover (LCL): Pieter Vanhuysse, Fund for Scientific Research, Flanders and London School of Economics Political Studies Association 2000. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA. 25

On Sen s Liberal Paradox Vanhuysse Politics (2000) 20(1) pp. 25 31 A: (Na,Nb) > (a,nb) > (Na,b) > (a,b) B: (a,b) > (a,nb) > (Na,b) > (Na,Nb) By L : B should be allowed to choose (Na,b) over (Na,Nb) By L : A should be allowed to choose (Na,Nb) over (a,nb) By P, however, (a,nb) is Pareto-superior over (Na,b) Thus, we have a cycle. Sen (1982a, p. 290) concludes his paper as follows: What is the moral? It is that in a very basic sense liberal values conflict with the Pareto principle If someone does have certain liberal values, then he may have to eschew his adherence to Pareto optimality. While the Pareto criterion has been thought to be an expression of individual liberty, it appears that in choices involving more than two alternatives it can have consequences that are, in fact, deeply illiberal (emphasis added). The influence of Amartya Sen s proof of this apparent liberal paradox has arguably been second only to that of the famous 1951 impossibility theorem by Kenneth Arrow, an earlier Nobel Prize laureate (see Arrow, 1963). In my view, the proof can be considered one of Sen s most important early (social choice) contributions to economics and social science in general, together with his truly outstanding later work on ethics and economics (e.g. Sen, 1987, 1988 and 1992a), poverty, underdevelopment and famines (e.g. Sen, 1981; Drèze and Sen, 1989 and 1995), and capability and well-being (e.g. Sen, 1985; Sen et al., 1987; Sen, 1993a). Sen s short 1970 paper spawned a massive literature within the field of social choice theory. Replying to part of this literature, Sen has, in a number of subsequent papers (Sen, 1982b, 1986, 1992b and 1993b), consistently argued that a variety of attempts to resolve this paradox, by modifying its main conditions or by interpreting them in different ways, all end in failure. But just like Arrow s proof, Sen s liberal paradox has also attracted strong interest from scholars outside the field of social choice. One of those, the political theorist Brian Barry, has provided a particularly strong critique of Sen s impossibility theorem. A political theorist replies: Brian Barry s critique The fact is, however, that the issue between Amartya Sen and Brian Barry is not at all about whether or not there is a contradiction between the P condition and the L condition as set out above (Barry does not deny this). Barry simply denies that Sen s L condition has got much to do with liberalism, properly understood, in the first place. By the second footnote of his 1986 paper, Barry has already summarised his entire position: There is no contradiction between saying it would be Pareto optimal for A to do x, and saying A has a right not to do x. We should simply reject the suggestion that our moral system has something wrong with it unless it generates the conclusion that if A exercises his right by choosing to do y then it must be a better (or socially preferred ) state of affairs in which he does y. My claim is not that condition L needs modification but that it is of an entirely inappropriate kind, forming as it does part of a social welfare function, to correspond to what liberals want to say about the importance of individual rights (1986, p. 11). Barry thus challenges the conception of liberty as put forward by Sen in the L condition. L states that each individual i should be socially decisive over at least one pair of alternatives concerning his private sphere (whether to paint his own kitchen walls pink or crimson, whether or not to read LCL, etc.): this implies that in these personal matters i is free to decide what should 26 Political Studies Association 2000

Politics (2000) 20(1) pp. 25 31 On Sen s Liberal Paradox Vanhuysse happen, and in choices over these things whatever i thinks must be taken to be better for society as a whole, no matter what others think (Sen, 1982b). Barry argues that a real liberal would have no reason for claiming that his decision in this personal sphere should also determine the socially better outcome, picked out by the social welfare function (SWF). Liberalism in his view is a doctrine not about what constitutes a socially better state of affairs, but about who has what rights to control what (Barry, 1986, p. 15). It picks out some matters as belonging to a person s protected sphere, in which his decisions are free from legal coercion, and lets the person be completely free in the use he makes of his right to decide upon those matters. Hence, there can be no real conflict between the P condition (which is about what is socially better ) and liberalism properly understood (which is about what people shall be free to do without legal coercion), unless of course one holds that what is socially better should always be enforced, in which case it is really rather absurd to speak about rights in the first place (what is, after all, the significance of having the right to do only what is socially better?). Thus, starting from Barry s view of liberalism, the issue between Barry and Sen on the impossibility of a Paretian liberal is actually more like a non-issue, or, as Barry later added (1991, p. 109), What the liberal paradox calls for is not solution but dissolution. Are social choice theory and political theory irreconcilable? Barry eagerly accepts, however, that under certain preference settings such as the Lewd and the Prude both having (strong) nosy preferences there can be a conflict between P and Sen s L condition. He argues (1986, p. 40) that this arises precisely from the fact that P and L both deal in outcomes and set up contradictory criteria for a socially better state of affairs. But this merely reinforces the point that condition L is not a liberal principle. What Barry does here is actually much more fundamental than tinkering a bit with the U, L or P condition, or engaging in a fancy semantic debate. What he offers, really, is a devastating critique of social choice theory. Somewhat mirroring I.M.D. Little s earlier critique of Kenneth Arrow s 1951 proof (see Little, 1973), Barry simply rejects as senseless the whole enterprise of aggregating individual preferences (going beyond individual want satisfaction to include also judgements over social welfare, right or wrong, etc.) into some sort of social welfare function, and of considering its outcome as a social welfare judgement, (bindingly) expressing what is better for society. He argues that: What we neither have nor could have is some algorithm for taking these divergent judgments and producing some social judgment. What we do need, in order to have a stable society, is a constitution that specifies how collectively binding decisions are to be taken. And if the society is to be liberal as well as stable, either the constitution or the legislation should set out individual rights. But this is, again, in the sphere of control, not the sphere of judgment (1986, p. 39). It would perhaps not altogether be such a bad idea to end my article here. This is so because Sen has, in my understanding, never convincingly rebutted the points raised by Barry s 1986 paper (see below). In fact, a great deal of Sen s arguments amount to saying that we need to broaden the informational base of the SWF to include much more than just utility information (e.g. the source of the preferences, whether they are meddlesome or not, etc.). Barry argues that this is an attempt to stop the mischief at too late a point. The move that should be Political Studies Association 2000 27

On Sen s Liberal Paradox Vanhuysse Politics (2000) 20(1) pp. 25 31 blocked is the one that treats moral or aesthetic judgments as preferences to be cranked into a SWF along with other preferences (1986, p. 35). Besides, one might ask how plausible such an infinitely broadened SWF really would be. Peter Hammond, for instance, concludes a 1982 paper (p. 102) by admitting that: It might seem like trickery to keep extending the domain of each individual s ultimate utility function further and further until it includes not only the usual social outcome, but also the history of the individual s tastes, expectations, and information. Well, it surely does seem like trickery to me. Moreover, the important collective choice problem avant la lettre, namely how to decide upon who may decide what, has surprisingly been left untouched by both authors in this debate. How should Barry s constitution come to specify how collectively binding decisions are to be taken or how to make a collective decision on what constitutes the individual s personal protected sphere? It may well be argued that the above question lies as such outside the scope of the formal debate between Barry and Sen. But that would in my view indeed render the whole debate quite futile, because what we have then is, first, the irrefutable technical proof by Sen on the incompatibility of the P and L condition (which has proved wide-ranging in its implications for the field of social choice) and, secondly, the strong political theory argument by Barry that the L condition has little to do with liberalism (which further implies that social choice theory is in fact quite unsuited to say anything about what really matters, and which leaves the whole matter to be decided by liberal theories of justice). It is therefore rather a shame that the two authors have not confronted each other more directly, especially since they have in other work elaborated on topics of some relevance to this debate (e.g. Barry, 1989 and 1995). One interesting insight on this matter, relating to the LCL case, is offered by Dennis Mueller: If all individuals were like A and B, and all books like LCL, it would be difficult to see how a liberal right to read what one wishes would ever emerge. In such a society, who reads what would be of concern to everyone and would presumably be treated as other public goodexternality decisions. If, however, most people are not like A and B and most books are not like LCL, then having to reach a collective decision on who reads what for every book and person in society would involve tremendous decisionmaking costs. Rational, self-interested individuals might agree to treat the choice of a book as a purely personal matter. Society economizes on transactions costs and thus is better off in the long run if each individual is free to make this choice himself (1989, p. 405). Liberty is the issue: two weak points in Sen s defence of his position Two weak points in Sen s subsequent defence of his position remain worthwhile discussing. The first point concerns Paretoimproving trades. Barry and others have argued that, given the nosy nature of A s and B s preferences, A s agreeing to read LCL in return for B s agreeing not to read it might constitute a mutually advantageous, and thus Pareto-improving, deal. Sen (1986, p. 226; 1982c, p. 345 and 1983, p. 27) remarks to this that (a) A and B might not want to enter such a contract. A and B might fail to act according to their preferences for ethical reasons, for instance because they give their liberal values a higher weight than their meddlesome preferences. Now, I am quite sure that no true liberal would have any problems with the 28 Political Studies Association 2000

Politics (2000) 20(1) pp. 25 31 On Sen s Liberal Paradox Vanhuysse fact that it cannot be presupposed that A and B must enter a mutually advantageous contract: the normative question of how to act in such a case is, after all, an entirely personal one. Thus, to Sen s remark (a), any liberal would presumably reply that it is precisely the liberal view that A and B have the right not to seek a Pareto-improving deal (they cannot be forced to do so); that, indeed, A and B might enter the trade (which would lead to a Pareto-improvement), or they might not for ethical or other reasons (in which case the P condition would be violated); but that, in the end, the liberal doesn t care too much anyway whether or not they enter the trade, as long as their rights are not violated by social coercion. What Sen seems to offer as a solution to the problem (namely that the Pareto principle should defer to liberty) is, for liberals, not even part of the problem: they do not attach any moral value to the Pareto principle. Sen furthermore remarks that (b) such a contract stipulating Pareto-improving trades might be difficult to implement and enforce. To this remark (b), Mueller (1989, pp. 404 405) replies that the costs of enforcing such a Pareto-preferred contract could prevent its realization even in the absence of liberal rights. If every decision as to who reads what had to be made as a collective agreement between A and B and neither had the right to do anything on his own, the prisoners dilemma nature of their preference structure would still provide incentives for both to cheat The second point concerns Sen s interpretation of the use of the L condition. Under Sen s specification of L, the constraint on social choice is linked to individual i s preference over some pair (x,y) of social states, i.e. of complete descriptions of all aspects of the society. However, under a more intuitive conception of individual rights, the individual enjoys the power to determine a particular aspect of a social state, whereby his choice with respect to this particular aspect imposes restriction on the final social outcome only in so far as, in the final outcome, that particular aspect must be exactly as he chose it to be (Gaertner et al., 1992, p. 167). If (and only if) each possible individual choice with respect to one aspect of the social state was linked to exactly one social state, then there would be a tight connection between such choice by the individual and his preferences over the social states. It is quite obvious, however, that such a tight connection does not always exist, as has been spelled out by Isaac Levi with regard to the LCL case (see also the compelling examples presented by Robert Sugden, 1985). Levi (1982, pp. 244 245) formulates the LCL payoff matrix as shown in Figure 1. b Nb a (1,4) (3,3) Na (2,2) (4,1) Figure 1 The LCL payoff matrix The Prude (A) has the liberal right to decide whether or not to read LCL (to choose between a and Na, that is). But, as Levi s game format shows, A s choosing Na is equivalent to choosing (Na and Nb) or (Na and b). It is choosing that a disjunction of social states be true, but not (contra Sen, 1982b) that one particular social state be true. Otherwise stated, a more plausible characterisation of individual liberty sees it as the right to determine a particular aspect of a social state, whatever one s preferences over complete social states, and whatever the social state that happens to prevail in the end. And when in the final outcome the Pareto principle is violated, so be it. For instance, in the LCL case, the Nash equilibrium (Na and b) is likely to prevail. Whilst this means that the P condition is violated, since both Prude and Lewd prefer (a and Nb) to (Na and b), this should be no cause for moral concern since both Prude and Lewd have exercised their liberal right in this more intuitive sense. Political Studies Association 2000 29

On Sen s Liberal Paradox Vanhuysse Politics (2000) 20(1) pp. 25 31 In sum, there seem to be some fundamental problems inherent in the social choice treatment of rights and liberties, as pointed out convincingly by a number of welfare economists (see e.g. Sugden, 1985; Gaertner et al., 1992; Kolm, 1994; Pattanaik, 1994). The political theorist Keith Dowding, finally, argues (1997, pp. 30 31) that social choice requires a function that specifies the outcomes, not the procedure by which the outcomes occur. As a consequence, in social choice terms it is impossible to make a distinction between, first, the social state in which a certain outcome occurs because the Prude chose to read LCL and the Lewd chose not to read it and, secondly, the social state in which the outcome occurs because the Prude was forced to read LCL and the Lewd was not permitted to read it (since in both social states the outcome is the same). It follows, says Dowding, that social choice cannot distinguish rights from powers, making an error which rights theorists have not made since the time of Hobbes. Which brings us back, in the end, to Barry s criticism of the social choice approach, above. Conclusion I have argued that Amartya Sen s famous proof of the impossibility of simultaneously satisfying the U, P and L condition (and thus of being a Paretian liberal) has proved very influential in the field of social choice theory. However, from a political theory angle on the one hand, and from a welfare economic angle on the other, Brian Barry and others have mounted a convincing attack on Sen s conception of liberalism in the 1970 paper. This furthermore implied a strong critique of the practice of social choice theory of aggregating individual preferences over social states into a binding social welfare judgement, and led to a fundamental doubt about the appropriateness of social choice theory to deal with philosophical issues of rights and liberties. These critiques seem to have put the burden of proof squarely in the camp of social choice theory as regards the fruitfulness of the SWF approach to individual freedom. Notes 1 I wish to thank Brian Barry, Keith Dowding, Patrick Dunleavy, Orsolya Lelkes, Thi Minh- Phuong Ngo and Toon Vandevelde for their helpful comments on an earlier version of this article. All errors remain my own. References Arrow, K.J. (1963), Social Choice and Individual Values (2nd edn), New Haven: Yale University Press. Barry, B. (1986), Lady Chatterley s Lover and Doctor Fischer s Bomb Party: Liberalism, Pareto Optimality, and the Problem of Objectionable Preferences in J. Elster and A. Hylland (eds.), Foundations of Social Choice Theory, Cambridge: Cambridge University Press, pp. 11 44. Barry, B. (1989), Theories of Justice, Berkeley: University of California Press. Barry, B. (1991), Paradox Lost, added paragraph to Lady Chatterley s Lover and Doctor Fischer s Bomb Party: Liberalism, Pareto Optimality, and the Problem of Objectionable Preferences in his Liberty and Justice: Essays in Political Theory 2, Oxford: Clarendon Press, pp. 78 109. Barry, B. (1995), Justice as Impartiality, Oxford: Clarendon Press. Dowding, K. (1997), Fairness in Political Choice: Equity, Rights and Votes (mimeo), London School of Economics. Drèze, J. and A. Sen (1989), Hunger and Public Action, Oxford: Clarendon Press. Drèze, J. and A. Sen (1995), India. Economic Development and Social Opportunity, Delhi: Oxford University Press. Gaertner, W., P.K. Pattanaik and K. Suzumura (1992), Individual Rights Revisited, Economica 59, pp. 161 177. Hammond, P. (1982), Utilitarianism, Uncertainty, and Information in A. Sen and B. Williams (eds.), Utilitarianism and Beyond, Cambridge: Cambridge University Press, pp. 85 102. Kolm, S.-C. (1994), Rational Normative Economics vs. Social Welfare and Social 30 Political Studies Association 2000

Politics (2000) 20(1) pp. 25 31 On Sen s Liberal Paradox Vanhuysse Choice, European Economic Review 38, pp. 721 730. Levi, I. (1982), Liberty and Welfare in A. Sen and B. Williams (eds.), Utilitarianism and Beyond, Cambridge: Cambridge University Press, pp. 239 250. Little, I.M.D. (1973), Social Choice and Individual Values in E. Phelps (ed.), Economic Justice, Harmondsworth: Penguin, pp. 137 152. Mueller, D. (1989), Public Choice II, Cambridge: Cambridge University Press. Pattanaik, P. (1994), Rights and Freedom in Welfare Economics, European Economic Review 38, pp. 731 738. Sen, A. (1981), Poverty and Famines: An Essay on Entitlement and Deprivation, Oxford: Clarendon Press. Sen, A. (1982a), The Impossibility of a Paretian Liberal in his Choice, Welfare, and Measurement, Cambridge, Mass.: Harvard University Press, pp. 285 290. Sen, A. (1982b), Liberty, Unanimity, and Rights in his Choice, Welfare, and Measurement, Cambridge, Mass.: Harvard University Press, pp. 290 326. Sen, A. (1982c), Personal Utilities and Public Judgements: or What s Wrong with Welfare Economics? in his Choice, Welfare, and Measurement, Cambridge, Mass.: Harvard University Press, pp. 327 352. Sen, A. (1983), Liberty and Social Choice, Journal of Philosophy 80, pp. 5 28. Sen, A. (1985), Commodities and Capabilities, Amsterdam: North-Holland. Sen, A. (1986), Foundations of Social Choice Theory: An Epilogue in J. Elster and A. Hylland (eds.), Foundations of Social Choice Theory, Cambridge: Cambridge University Press, pp. 213 249. Sen, A. (1987), On Ethics and Economics, Oxford: Blackwell. Sen, A. (1988), Freedom of Choice: Concept and Content, European Economic Review 32, pp. 269 294. Sen, A. (1992a), Inequality Reexamined, Oxford: Clarendon Press. Sen, A. (1992b), Minimal Liberty, Economica 59, pp. 139 159. Sen, A. (1993a), Capability and Well-being in M. Nussbaum and A. Sen (eds.), The Quality of Life, Oxford: Clarendon Press, pp. 30 53. Sen, A. (1993b), Liberty and Social Choice in W.J. Booth, P. James and M. Hudson (eds.), Politics and Rationality, Cambridge: Cambridge University Press, pp. 11 33. Sen, A., J. Muelbauer, R. Kanbur, K. Hart and B. Williams (1987), The Standard of Living, Cambridge: Cambridge University Press. Sugden, R. (1985), Liberty, Preference, and Choice, Economics and Philosophy 1, pp. 213 229. Political Studies Association 2000 31