Pedro Schwartz

The Poverty of Social Choice

Pedro Schwartz*

The ballot box produces unanimity without conformity; the marketplace, unanimity without uniformity.
Free to Choose, Milton Friedman and Rose Friedman

The search for a method of collective decision-making to solve social problems in a rational manner is the Holy Grail of American liberals and European social-democrats. But precisely the contrary is to be desired: the fewer the decisions individuals have to take collectively the better it is. The contemporary version of this limitless rationalism, unafraid of turning everything into politics in the name of civic republicanism, is the so-called "theory of social choice", that we associate with the names of Kenneth Arrow and Amartya Sen, both winners of the Nobel Prize. In this column I wish to suggest that 'Social Choice' is at best barren, at worst dangerous.
The Old Welfare Economics

'Social choice' has its roots in the Utilitarian philosophy and in its offshoot welfare economics. Jeremy Bentham, James Mill and the young John Stuart Mill tried to define the general welfare as the sum of the net pleasure or utility of individuals in a society, under two assumptions: that each person counted for one; and that it was possible to compare the utility of one person with that of another.1 The insistence by John Stuart Mill (1861) that there were higher and lower pleasures—"better Socrates dissatisfied than a pig satisfied"—was a step in the direction away from Benthamite interpersonal comparison: people were too different to be added up, was the implicit conclusion in Mill's thought. Despite Mill's doubts, he himself and later economists insisted in their search for ways of aggregating utilities to formulate public policy scientifically. So they looked for a new criterion of general welfare that would avoid the interpersonal comparisons that Mill found so difficult to normalise.2

Thus, at the very end of the 19th century, Vilfredo Pareto proposed a welfare criterion that did not need each individual to calculate her personal utilities and which would allow an "outside arbiter" to compare and aggregate the measured utilities of individuals. The Pareto criterion was based on individuals classifying their preferences ordinally; and such social situations as were unanimously accepted could be taken as based on a value judgments accepted by all.3 True, the unanimity posited by Pareto was minimal, valid with whatever number of abstentions or as the Latin sentence goes, nemine discrepante. A 'Pareto' improvement took place when at least an individual bettered her situation and no one saw any worsening of theirs.4 Hence, the Pareto criterion is incomplete. It does not attempt to order all possible social situations and policy changes, as it says nothing about changes where some are improved but others lose. Also, it sets aside considerations of distribution, since a Pareto improvement is to be preferred even if the person bettered is a super-billionaire and the situation of all others is unchanged. Still there is a quite large set of situations that are Pareto-acceptable: all trades in a free market make the two parties to the exchange better off, and the rest stay as before.5

A different line of defence of welfare calculus was then tried by Arthur Pigou. Mill had carefully examined the exceptions to the rule of laissez faire in his Principles of Political Economy6 (1848) when defects in the market needed correction.7 Pigou progressively expanded Mill's list of permitted state interventions in The Economics of Welfare8 (1920). Pigou started from the ideal of a perfect market, then listed the deviations from perfection in reality, and finally proposed taxes and subsidies to correct them. Every edition of that book had a longer list of market failures and a wider remit for public regulators. Thus, the Pigovian analysis looked increasingly ad hoc, as a pile of excuses for state interventions rather than a theory of public policy.

Next a devastating critique by Lionel Robbins intervened. Robbins issued an interdict on the comparison of utilities among persons that were needed for the calculus of social welfare. Strictly speaking as he pointed out (1932-35), full interpersonal comparisons of happiness are impossible. This is so for two reasons: (1) it is impossible to measure utility for each person, since that (cardinal) number will not be invariant to the chosen units; and (2) comparing the self-perceived states of happiness between persons is also strictly impossible, if only for differences in keenness or sensitivity of feeling.9

The New Welfare Economics

The old welfare economics, especially in its utilitarian form, was declared insufficient. Even the Pigovian 'market defects' program was seen to lack a formal basis. The Robbins critique had left the Pareto criterion unscathed because unanimity, even in its weak nemine discrepante form, demanded no cardinal measurement nor interpersonal comparisons of happiness. So welfare economics was formalised with the help of the Pareto criterion. The starting point was again the ideal of the perfect market and a new welfare economics was formulated summed up in two propositions:

  1. I. Any competitive equilibrium is Pareto optimal
  2. II. Any optimal production plan chosen by a planner can be achieved via the operation of the competitive market.

These two propositions look the same to the unwary but they are not. They set the framework for a 'scientific' theory of public policy for the following fifty years, thus:

  1. I. A. Since the actual capitalist markets were never competitive and never in equilibrium, there was constant need for policy intervention to achieve a Pareto optimal economy.
  2. II. B. The just society could be created by a politically defined Plan and this Plan could then be put into effect by trusting its execution to a competitive market.

The first proposition was interpreted to imply that a well-planned socialist economy could approach Pareto optimality much better than the capitalist market. The second proposition was seen as indicating the possibility of a division of labour between planner and market to create an optimal socialist commonwealth. These two theorems of the new welfare economics were first outlined by Enrico Barone (1908) and analytically proven by Oskar Lange (1942).


For more on these topics see "The Vacuity of the Political 'We'," by Pierre Lemieux, October 6, 2014, " Collective Choice at Work," by Anthony de Jasay, December 3, 2012, and "The Dangers of Majoritarian Democracy," by Pedro Schwartz, December 5, 2013, at the Library of Economics and Liberty.

The title of Barone's essay has sinister connotations for the generations who have known fascism and communism: "The Ministry of Production in a Collectivist State". Barone wanted to show that a collectivist government could: (1) lead society to a productive optimum;10 and (2) redistribute what, in an "individualistic regime", the capitalists would themselves have consumed after reinvesting the larger part of the profit. The planner would attain (1) by discovering the most economical combinations of factors11 through trial and error by means of price changes. As for (2), the planner would redistribute the surplus according to the egalitarian preferences of the people. In sum, the planned economy would function exactly as a perfect individualist market economy, where costs of production are at their minimum and are equal to price, and the only two socialist traits of this economy would be the collective ownership of the means of production and the egalitarian distribution of the surplus previously consumed by capitalists.12

Of course, as Ludwig von Mises and F.A. Hayek pointed out, Barone's socialist economy relied on a number of unspoken assumptions about how well informed the planner could be. (A) The planners would know the full effects of any price changes on the current combinations of factors, actual and potential, allowing them to set, choose, or modify them for the convenience of the plan; (B) the planners would know what consumption goods individuals could want and choose and accordingly change their prices to avoid shortages or surpluses; (C) the planners could also tune the rate of interest on saving so as to guarantee investment for growth; and (D) the populace would know and acquiesce in the distribution of the surplus decided by the state. The impossibility of gathering such knowledge made Barone's proposal unworkable, as it would Lange's.

Lange, who was an admirer of Stalin, applied these theorems to formulate his own version of 'market socialism". In a planned economy, the Communist government could define the objectives of the Quinquennial Plan (including its social objectives) and then play with the prices in a mock competitive market so as to equalise the supplies of and demand for the final goods and services: the planner would ask producers how much they would supply given a schedule of prices, and ask consumers what they would pay for the different quantities supplied. After much toing and froing this would throw up the equilibrium point at which the market would empty.

As I just said, Mises and Hayek (1920 and 1935, respectively) showed the theoretical impossibility of such arrangements, for two reasons: one that gathering the necessary information about the millions of prices and their changes in a market economy was impracticable; the other, that in any case producers and consumers would have an interest not to reveal their preferences to the planner.13 I well remember a lecture by Oskar Lange at the Old Theatre of London School of Economics a few months before his death in 1965. Lionel Robbins was in the chair. Lange explained how computers would make the calculations of market socialism workable. Robbins, who sat above Lange, could barely contain his laughter. The collapse of 'real socialism' in 1989 confirmed the accuracy of the critics' judgement.

Social Choice

It is with trepidation that I enter the field of collective choice with critical intent, a field bristling with Nobel Prize winners and knowledgeable experts in mathematical logic. As a former pupil of Amartya Sen, I aver that I have found few teachers as inspiring as he was. He kept the class spell-bound for two hours at a stretch while covering the blackboard with deductions and proofs of mathematical logic. He was courteous to a fault and sworn to reason and compassion. Whatever I say here about his welfare theory should not be understood as derogation of the respect I feel for him as an economic philosopher.

Finding Barone and Lange in a cul de sac, the defenders of collective choice felt the need for a method to formulate and evaluate public policies from the standpoint of methodological individualism and not as the dictates of an outsider planner. This new path was opened by Abram Bergson (1938) and Paul Samuelson (1947) who defined the general structure of ways to organise society rationally by means of methodologically acceptable transformations of individual preferences into social preferences. The transformations are usually known as social welfare functions (SWFs). The transition from individual to social should fulfil two conditions: (a) that the SWF be strictly related to the welfare of individuals, so that, when the situation of individuals is bettered, the SWF also shows an improvement; (b) that any of these SWFs arrange all resulting social states in an order going from worse to better unequivocally. Within these wide limits philosophers would able to adjudicate among proposed SWFs as to which would best aggregate the ethical demands of individuals, and thus judge the justice or fairness of a market economy.

The welfarist party then received a cruel blow from Kenneth Arrow (1952), one of its foremost champions: the "Arrow impossibility theorem". This theorem proved that no SWF could exist that fulfilled four very mild conditions: that it be applicable to all conceivable choices; that it be unanimous; that it be chosen on its own merits; and not be imposed by any one person on the rest.14 The conclusion was devastating: Arrow had proved that it was impossible for a society to agree on a welfare arrangement, even if the individuals of that society unanimously preferred it. As Andreu Mas-Collell put it (1974): a social group that may try to apply a SWF will inevitably find that "it cannot decide rationally, that is to say, as if it were an individual person".

It is instructive to follow the twists and turns of the whole collective choice school to try and salvage some part of 'rational' welfare economics, broadly understood to include public economics, planning theory, the theory of the state and the theory of social justice. To this purpose, the school showed that the rules to be applied could work reasonably well if preferences are restricted. Also, the limitations of Pareto unanimities as regard the distribution of income and wealth could be partially overcome if levels of interpersonal comparisons were in some way allowed. And the non-dictatorship condition could be suspended for decisions affecting essential liberties, when an individual had the right to veto some social injunction.

In the end and after much logical demonstration, Sen himself admitted (1970) that there can be no single golden rule to organise society along welfarist lines. His book, said Sen,

... has been concerned with impurities of one kind or another, e.g., partial interpersonal comparability [...], partial cardinality [...], restricted domains [...], intransitive social indifference [...], incomplete social preferences [...], and so on.

With a humorous turn typical of his seductive personality, he ends by saying that,

... while purity is an uncomplicated virtue for olive oil, sea air, and heroines of folk tales, it is not so for systems of collective choice.

Robbins Again

In the Preface of his 1970 book, Sen perhaps unwittingly makes what I think is a crucial separation between questions of the theory of decision procedures and questions of political philosophy. For me, the main contribution of social choice is the discovery and attempted solutions for the conundrums and contradictions of decisions taken by bodies of people; and the main danger of social choice is the attempt to define a just society and impose it on people. Of course, we do have to take communal decisions. Their structures and results are not evident. Their logical mechanisms have to be explored, as when we analyse the paradoxes of voting or the pervasive free-riding that besets public goods. But these factual studies must not be confused with the ethics of collective decisions.

Sen ingeniously rebuts Robbins's interdictum of interpersonal comparisons of utility by noting that the prohibition against comparing preferences interpersonally may be lifted if those involved are ready to take the consequences of their choices into consideration when debating whether to hold onto their preferences. They are implicitly taking those values and preferences as "non-basic", that is to say, ready to temper them or to give them up in the name of justice. "It should be fairly obvious", he says, "that nothing much of interest can be said on justice without bringing in some interpersonal comparability". (1970, page 150). This is not the definition of justice according to Hume, as we shall see.

"Citizens make social choices, but there cannot be a 'Social Choice'."

By outlawing inter-personal comparisons in welfare economics, Robbins precisely wanted to defend an Austrian view of justice in society. In an individualistic market system one cannot say that society is just or unjust, nor that rewards are undeserved or the distribution of property unfair. It is people who are just, not systems. Of course in democracies we make social choices, according to the interests and the moral judgment of the different individuals concerned. These judgments can be evaluated or criticized by pointing to their effects, self-contradictory or positive. 15 This is very different from trying to formulate and apply a social welfare function, however modified to avoid 'Arrow contradictions'. Citizens make social choices, but there cannot be a 'Social Choice'.

This refusal to make collective social judgments is clearly in the tradition of David Hume, who in (1752) defined two moral duties that men and women perform entirely from a sense of obligation, only in consideration of "the necessities of human society, and the impossibility of supporting it, if these duties were neglected."

It is thus [that] justice or a regard to the property of others, [and] fidelity or the observance of promises, become obligatory, and acquire an authority over mankind. (Hume, Essays Moral, Political, and Literary, page 48016)

If we stand by Hume, the whole endeavour of collective choice belongs to a world of collective dreams that can easily turn into nightmares. Collective choice moves in a world without institutions, without competition, without history; a rational world of decisions based on perfect knowledge of individual preferences.

The danger is that some arbiter may start acting on the basis that he knows what is best for others.17 Sen defined individual liberty as including the enjoyment of what he called "functionings"—enough food, good health, a long life, opportunities for happiness, respect for one's dignity, participation in the life of the community. There is a telling passage in which he laments the situation of downtrodden people in an unfair society, who may go hungry, die young, lose most of their children, lack education, suffer discrimination, and not even know that they are in want of the minimum capacities to function. They neither control their lives nor have a capacity for personal-choice, he says. So he defends the

... social-choice characterisation of liberty [which] compares what [in fact] emerges with what the person would have chosen, whether or not he actually does the choosing18.

I understand this as meaning that we can impose liberty on people who are too poor or too ignorant to make the choices we think are right for them. These fateful words conjure the shadows of Indira Ghandi's forced sterilisation or the 'one child policy' of Communist China.

One of the objects of Sen's Collective Choice and Social Welfare (1970) is to show that it is impossible to be a classical liberal and present the free market as one of the few social arrangements where unanimity rules. His "Impossibility of a Paretian Liberal19" encapsulates in one expression this alleged paradox. An emergent solution to this paradox and many others in social choice is an institution evolved in our societies since Roman times, namely, private property. This institution partitions the domain of Paretian rules so that for the things she owns she can exercise a veto against the decision of the rest of society, which is the essence of human liberties (or 'human rights' as they are usually called). The preservation of private property in Western societies is not only helped by its positive effects on productivity, as in the end, through purchase or rent resources will fall into the hands of the most efficient user. Property rights also help protect individual liberties.

Market Defects Corrected by Emerging Institutions

The eternal argument of interventionists and regulators against a free economy is the existence of market defects. They seem not to have read Ronald Coase or to have been taught his (1960) theorem in its static formulation. Coase in his later years moved away from the interpretation of his theorem as showing that alleged market defects dissolved on condition that property rights were clearly defined and the economy was perfectly competitive. Welfare improving trades created property rights and functioned under imperfect competition—a shining example being the growth of capitalism in con temporary China. On this point I need not repeat myself, since I argued it at length in a Letter from Europe published at the Library of Economics and Liberty in October last year, under the title "Ronald Coase, the Unexpected Economist".20 So I can refer my readers to that unconventional piece of mine.


Bentham, Jérémie (1802): Traités de legislation civile et pénale. Étienne Dumont, ed. Second edition, 1820. Bossange, Paris.

Berlin, Isaiah (1969): Four Essays on Liberty. OUP.

Coase, Ronald (1960): "The Problem of Social Cost"1-44., Journal of Law and Economics, nr. 3, October, pgs. 1-44.

Hayek, Friedrich A., ed. (1933, 1935): Collectivist Economic Planning. Routledge & Son, London.

Hume, David (1752, 1986): "Of the Original Contract", Essay XII of Essays Moral, Political, and Literary. Part II. Liberty Fund. Indianapolis.

Lange, Oskar (1936-37): "On the Economic Theory of Socialism", Parts I and II. Review of Economic Studies, vol. 4, nr. 1, October, pgs. 53-71; vol. 4, nr. 2, February, pgs. 123-142.

Lange, Oskar (1942); "The Foundations of Welfare Economics". Econometrica, vol. 10, nrs. 3-4, July-October, pgs. 215-228.

Lawrence, D.H (1928, 1960): Lady Chatterley's Lover. Penguin. Hammondsworth.

Mas Colell, Andreu (1974): "Introducción" a K.J. Arrrow: Elección social y valores individuales. Instituto de Estudios Fiscales, Madrid.

Mill, John Stuart (1861): Utilitarianism. In Collected Works, vol. X. University of Toronto Press (1969).

Mises, Ludwig (1920, 1935): "Economic Calculation in the Socialist Commonwealth", in Hayek, ed. (1935). First published in German in Archiv für Sozialwissenschaften, Tübingen.

Pareto, Wilfredo (1897): Cours d'économie politique. Rouge, Lausanne.

Pigou, Arthur (1920): The Economics of Welfare. MacMillan, London.

Ramsey, Frank: "A Mathematical Theory of Saving", Economic Journal, vol.38, pgs. 543-559.

Robbins, Lionel (1932, 1935): An Essay on the Nature and Significance of Economic Science. MacMillan & Co., London.

Schwartz, Pedro (1972): The New Political Economy of J.S. Mill. Duke University Press.

Sen, Amartya (1970): Collective Choice and Social Welfare, Oliver & Boyd, Edinburgh.

Sen, Amartya (1983): "Liberty and Social Choice", in Journal of Philosophy, 80, January.


The object of Bentham's legal philosophy was to help societies attain the greatest aggregate happiness. For that one needed to calculate the net sum of pleasures and pains caused by laws and policies. Since the sensibility of men varies according to age, sex, education, fortune, religion and the other circumstances that influence it, Bentham created an elaborate system of utility measurement or "felicific calculus"" so that personal utilities could be added to obtain social utility. The importance of such a scale of comparison for utilitarianism was rightly underlined by the Etienne Dumont in his influential edition of Bentham's works in French (1802, 1820). For more on Bentham's philosophy, see my June, 2015 column, "Jeremy Bentham's Mistaken Universalism."


Mill's difficulty could not be solved by 'felicific calculus' because he could not agree with Bentham that the stuff of happiness was the same for everyone, only modified by circumstantial accident, such as intensity, remoteness of probability. He could not agree with Bentham's dictum that "pushpin is as good as poetry". At bottom Mill was saying that the happiness of different people was incommensurable. His solution was paternalistic: people who were able to feel both highbrow and lowbrow happiness could adjudicate on the real worth of different sources of happiness. It is lucky that Mill lived in Victorian times when le plaisir de la boue was inconceivable or at least not respectable.


Sen, Collective Choice and Social Welfare (1970), pages 57-58.


As Sen (1970) put it: "x is Pareto-optimal if we cannot choose an alternative that everyone will regard to be at least as good as x and which at least one person will regard to be strictly better than x," page 21.


Though any trade between two persons nemine discrepante changes relative prices and thus affects the rest, the information transmitted by prices is precious and welfare-neutral. For example, if I sell my house and somebody buys it, the prices of all other house in the market are somewhat changed. A third party may feel harmed by this indirect effect on the value of her assets. But price movements simply transmit information on things as they are and as such are neither just nor unjust.


Schwartz, The New Political Economy of John Stuart Mill (1972), pages 129-142.


The Economics of Welfare , by Arthur C. Pigou. Library of Economics and Liberty.


This is as explained in Sen (1970). Below, we shall see Sen trying to rescue interpersonal comparisons by speaking of broad levels of utility; and in fact misunderstanding Robbins's interdictum.


Barone defined the collective maximum in Paretian words, as a situation where every further modification would place individuals in a worse position.


Following Leon Walras, he calls these combinations of factors "technical coefficients". Some of these could be varied by the planner by trial and error so as slowly to bring the economy nearer to the collective maximum welfare.


Either making the portion equal for each individual; or equal for classes of individuals.


This is impossible even today with 'big data' methods: not only the gathering of the data, but interpreting them and their interconnections needs of an accurate model of the whole economy. And we know what we think of multi-equation models of large economies.


Sen (1970). More precisely: (1) that the welfare function in question "should work for every logical configuration of individual preference orderings" (Condition U of unrestricted domain); (2) that the SWF in question satisfy a very undemanding form of the Pareto principle, to wit, "if everyone prefers x to y, then society must also prefer x better than y" (Condition P); (3) that the decision of x over y should be influenced by no other consideration but of these two states (Condition I, of independence of irrelevant alternatives); and (4) that no one person should decide for society "irrespective of the preference of everyone else" (Condition D, of non-dictatorship). In class Sen formulated the mnemonic device "stupid" to remember these four conditions.


Sen distinguishes between "basic values", for which we are ready to die, from "non-basic values", which we might give up if their consequences in certain circumstances are self-defeating or cause unacceptable harm to others. In the latter case, an interpersonal comparison is implicitly being made.


Essays, Moral, Political, and Literary , by David Hume. Library of Economics and Liberty.


Note the "outside arbiter" on page 100 of Sen (1970). Despite Sen's methodological individualism, which made him lay down that all social choices must be reducible to individual preferences and decisions, there is a strong whiff of an outsider above the fray adjudicating among individual choices.


Sen, "Liberty and Social Choice." Journal of Philosophy, 1983, page 454.


For a description of Sen's Lady Chatterly example, see my July 2015 Econlib column, "Lady Chatterly's Lover, or the Poverty of Social Choice."


"Ronald Coase, the Unexpected Economist," by Pedro Schwartz. Library of Economics and Liberty, October 7, 2013.

*Pedro Schwartz is "Rafael del Pino" Research Professor of economics at Universidad Camilo José in Madrid. A member of the Royal Academy of Moral and Political Sciences in Madrid, he is a frequent contributor to the European media on the current financial and social scene. He currently serves as President of the Mont Pelerin Society.

For more articles by Pedro Schwartz, see the Archive.
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