Humane Studies Review

Volume 7, Number 1 Winter 1991/92

Suckers, Free Riders, and Public Goods

by Robert Sugden

Book Review

A review of Anthony de Jasay' s, Social Contract, Free Ride (New York: Oxford University Press, 1989)
In political and economic theory, it is a commonplace to say that government is necessary because of the existence of public goods. These are goods which everyone wants but which, because of the free-rider problem, it is not in anyone' s interest to bear the costs of supplying. This justification for government dates back to Hobbes, who argued that civil order was a public good that could be supplied only by a sovereign with a monopoly in the use of force. Thus, according to Hobbes, rational individuals in a " state of nature" would enter into a social contract by which each would submit to an absolute sovereign, provided everyone else did the same. Modern contractarian writers, such as John Rawls and James Buchanan, have developed variants of this argument to justify governments which, although subject to more constitutional constraints than Hobbes' Leviathan, are responsible for producing a wider range of public goods. In this ambitious book, Anthony de Jasay tries to show that this whole line of argument is a mistake: " there is no public goods problem in Hobbes' fatal sense" (p. 4).

The book starts well, with a broad-brush critique of the contractarian view of the state. Jasay proposes a two-way classification of political and economic relationships: there are relationships of contract and ones of command. In the case of contract, there is a presumption of mutual benefit; in the case of command, there is not. In opposite ways, Marxists and contractarians conceal this distinction. Marxists claim that wage contracts in a capitalist society are instances of command: sellers of labor may appear to be free, but really they are coerced. Contractarians claim that our submission to government is an instance of contract; we may appear to be subject to command, but really we have (or it is as if we had) agreed to the rules that we are compelled to obey. Jasay asks us to reject both claims as " special pleas" (p. 17). In particular, we should see Hobbes' contractarianism as an historically located special plea for the strong states which established themselves in Europe after the Middle Ages.

In a brief but powerful section of the book, Jasay offers us a picture of the late Middle Ages as a golden age of economic development and dispersed power. Contracts were enforced by self-help and by a variety of quasi-judicial institutions with overlapping jurisdictions; there was no single Hobbesian sovereign. It is an historical fact that a system of strong states displaced this more anarchic order, and this fact requires explanation, but we have no reason to presume that the change was generally beneficial. Jasay suggests instead that strong states were parasitic on their host populations; they established themselves by military force, which they used to disarm rival centers of power and to enforce their commands. From this perspective, contractarianism is an ideology which, by presenting command as disguised contract, serves to reconcile people to an irrevocable loss of independence.

In the main part of the book, Jasay takes on modern contractarian theories more directly, arguing that they fail on their own terms. This part of the book is much less successful. Jasay has little sympathy with modern work in political science and economics, which is " increasingly dreary" and pursues " technicalities of dubious import" (p. 8). Yet the core of the book is an abstract theoretical model, of precisely the kind that economists use. Given that he has chosen to work with such a model, and that he is trying to show that the standard conclusions of public goods theory are invalid, we are entitled to expect him to have mastered the technicalities of economic theory, however dreary he may find them. But he seems to have made little attempt to come to grips with the existing theory, and repeatedly takes short cuts rather than pursuing the logic of his own model. As a result, he makes crucial mistakes. His main conclusions, I think, are wrong.

In one standard model of the public goods problem, there is a single public good which is finely divisible. A group of many individuals jointly derive utility from the public good, with each person' s utility being a continuous and increasing function of the quality of the good that is being supplied. Each person is free to choose how much, if anything, to contribute towards the cost of supplying the good; the amount supplied is determined by the total of everyone' s contributions. Thus, if each person takes the behavior of the others as given, she can see that the net effect of her own contribution is to bring about only a small increase in the supply of the public good, the benefits of which are divided among all individuals in the group. Because each contributor pays for benefits which accrue mainly to others, it is typically not in anyone' s interest to contribute anything: this is the public goods problem. Jasay accepts the validity of this analysis, but questions the realism of the assumptions of the model. He does not question the assumption that each person pursues her own interests, taking the behavior of the others as given. (He does not claim that this provides a true picture of human motivation, but says that " the least semblance of founding our argument on the decency, far-sightedness, and considerateness of human nature must be avoided" [p. 126]. Any theory of public goods, he says, should be robust enough to cope with selfish behavior.) Instead, Jasay challenges the assumption of continuity, arguing that public goods are intrinsically indivisible.

At this point, I run into a difficulty. It is hard to give a brief summary of a complex argument that one believes to be fallacious. Roughly, the argument goes as follows. A public good, by definition, is a good that is supplied jointly to a group of individuals, with no one being excluded from the benefits. But if non-exclusion is to mean what it says, enough of the public good must be supplied so that there is no (or not too much) congestion among consumers; extreme congestion is a form of exclusion. Hence a " public good has a critical supply; less of it causes crowdedness and jeopardizes non-exclusion, more produces questionable additional benefit" (p. 144-45). In response to the thought that crowdedness is itself a continuous variable, Jasay offers the argument that " at a given level of civilization, with habitual norms and habits in the use of private substitutes, a community is likely to have reasonably specific ideas about the standard that public provision of a good must meet" (p. 160). He then gets sucked into the Sorites paradox (when does a pile of stones become a heap?) as he tries to maintain that each public good has a definite threshold of " critical supply," even if it is impossible for us to be sure where it is.

This whole argument seems to me to miss the point. Consider the example of parks in a city. Take a park to be an area of open ground which everyone is free to use. Then the quantity of parkland is measurable on a continuous scale (say, hectares). As the area of parkland increases, parks will become less crowded, more pleasant, and more varied. Thus we should expect each person' s utility to increase continuously as the area of parkland increases; there is no obvious reason to expect sudden discontinuities. This is all that the conventional theory of public goods requires. If the supply of parks was determined by the total of individuals' voluntary contributions to a park fund, and if everyone acted according to self-interest, there would be a free-rider problem. Of course, if total contributions were very small, the " parks" would be overcrowded, trampled areas, and we might argue about whether they could properly be called parks. But even if we decide they must be called something else, say " public open space," there is no exclusion in the sense that matters for economic theory. All that matters is that no one is excluded from the benefits created by an increase in the supply of the good.

The existence of discontinuities matters to Jasay because he believes that there is no public goods problem for indivisible goods. He begins by considering a game in which there is an indivisible public good and two potential contributors. Each player has to choose one of two strategies, " subscribe" or " not subscribe." For each player, there are four possible outcomes: that he subscribes while the other does not (S, the " sucker" outcome), that the other subscribes while he does not (F, the " free rider" outcome), that both players subscribe (M, the " fair mixed regime" ), and that neither subscribe (E, the " exchange regime" ). If each player' s preference ranking, in descending order, is (F, M, E, S), then we have the familiar Prisoners' Dilemma, in which not subscribing is the dominant strategy. But Jasay asks us to consider the case in which each player' s ranking is (F, M, S, E). He calls this the " straddle" ranking; economists and game theorists will recognize it as the game of Chicken. In this case, there is no dominant strategy. Each player prefers not to subscribe if he expects the other to subscribe, but prefers to subscribe if he expects the other not to do so. What each person will do will depend on his estimate of the probability that the other will contribute, and on his own attitude toward risk. So if the problem takes the form of a Chicken game, it is possible that self-interested individuals might choose to contribute towards the cost of supplying the public good. There might still be free riders and suckers, but (Jasay seems to suggest) the suckers would have no grounds for complaint. A sucker is someone who chose to subscribe because he judged this choice to be in his own interests: he could have chosen not to subscribe, as the free rider did, but preferred not to take the risk.

This analysis provides the kernel of Jasay' s attempted resolution of the public goods problem. But, as he says, the two-person model is " a reference framework only" (p. 138); if he is to succeed in his objective, he must extend the analysis to the case of a public good with many potential contributors. The way in which he tries to do this can be explained by means of an example.

Consider a public good that is genuinely indivisible. Suppose a private collector offers a famous painting to a public gallery for a fixed sum of money; if the gallery does not pay, she will export the painting. The gallery has no funds of its own, but launches an appeal to raise the money. Here there is a public good with an obvious " critical supply." Jasay proposes a procedure for supplying public goods like this from individual contributions. With only slight simplification, we can represent this procedure by the following model.

Suppose the cost of the painting is 100 units. The fund-raisers invite individuals to make " pledges" ; a pledge is a promise to pay up to 2 units towards the cost of the painting. If less than 50 individuals come forward, the pledges are not called up. If 50 or more individuals come forward, the painting is bought, and the cost is divided equally among those who have pledged money. Clearly, this procedure has an advantage over the one assumed in the standard model of public goods; it sets limits on the extent to which anyone can be made into a sucker. Free riding is still possible (you may not make a pledge, while 50 or more others do), but no one will have to pay anything unless at least 49 other people do so. More importantly for the theory, non-contribution may not be the dominant strategy.

Suppose there are 100 identical art-lovers, each of whom would gain a benefit of v if the painting were acquired by the gallery. Assume that v is greater than 1, so that everyone would be better off if everyone pledged money than if no one did (that is, provision of the public good is Pareto efficient). Now consider any one individual who is deciding whether or not to make a pledge, without knowing what the others are doing. From his point of view, there are three possibilities: the number of other people making pledges may be less than 49, exactly 49, or more than 49. In the first case, it does not matter what he does: the fund will not reach the target. In the third case, the painting will be bought whether he makes a pledge or not, so it is in his interest to take a free ride. But in the second case, whether or not he makes a pledge will determine whether or not the painting is bought. By making a pledge he incurs a cost of 2 (his share of the cost when there are exactly 50 pledges) and gains v (the benefit of the painting to him). In this case, the individual' s contribution is not (as Jasay says of contributions in the standard model) a mere " driblet," whose benefit is spread over many individuals, but is decisive in getting the public good supplied at all. Thus, provided v is greater than 2, non- contribution is not a dominant strategy: there are circumstances in which an individual would benefit by contributing.

So far, so good. But now Jasay takes a series of illegitimate short cuts. He asserts that " broadly speaking," if a person thought that most other people would not make pledges, it would pay him to make a pledge, while if he thought most other people would make pledges, it would pay him not to (p. 154). He seems to see this as showing that there is a symmetry between pledging and not pledging. Somehow, he manages to avoid any use either of the theory of probability or of the standard game- theoretic concept of a mixed-strategy equilibrium. (Failing to find what a game-theorist would call a pure strategy equilibrium, he gets bogged down in the " all Cretans are liars" paradox; his attempts to escape are not entirely convincing.) It is not quite clear what conclusion Jasay wants to draw from his model, but presumably he wants to claim that in typical cases, enough pledges will be made for the public good to be supplied. (Recall that the whole point of the book is to show that there is no public goods dilemma.)

Would it pay an individual in the model to make a pledge? If we are to answer this question properly, we must ask how probable it is that exactly 49 other people will make pledges (the case in which it pays to make a pledge), relative to the probability that more than 49 will make pledges (the case in which it pays to free ride). Let us call this the critical ratio. Given the probability that any one person will make a pledge, working out the critical ratio is a straightforward theoretical exercise. For example, if each person is as likely to make a pledge as not, the critical ratio is approximately 0.16. So unless v, the value of the public good to the individual, is large, it will pay an individual to take a free ride. It turns out that v must be greater than 13.5 in order for pledges to be worthwhile in this case. In other words, the total benefit of the public good must be 13.5 times greater than the total cost. If v were equal to 13.5, then, it would be possible to have an equilibrium in which each individual was indifferent between pledging and free riding, and in which the probability that any individual made a pledge was 0.5. Then there would be a slightly better than even chance (0.54, to be precise) that the public good would be supplied. This is not a particularly reassuring conclusion to draw about a case in which the benefits of the good are so many times greater than the costs.

If the ratio of benefits to costs was smaller, the probability that the public good would be supplied would be correspondingly less. If, for example, the benefits of the public good were five times greater than the costs, the probability of its being supplied would be less than 0.03. If the benefits were twice the costs, the probability of its being supplied would be zero.

Of course, these are little more than back-of-the-envelope calculations, using very specific assumptions. But there is a perfectly clear general principle behind them. It pays to make a pledge only in the event that the number of other people making pledges is exactly equal to some critical value, while it pays to free ride in the event that there is any larger number of pledges. If there are many individuals and if there is to be a reasonably high probability that at least the critical number of pledges will be made (and thus a reasonable chance that the public good will be supplied), the probability of the first event must be low, relative to the probability of the second. This is an inescapable consequence of the laws of probability. And so it will not be in anyone' s interest to make a pledge unless the benefit she derives from the public good is much greater than her share of the costs.

So it seems that Jasay' s line of enquiry is not going to provide an escape from the public goods problem. If I am right, the central project of the book must be judged a failure. Nevertheless, Jasay is right to remind us that public goods can sometimes be provided without the intervention of a Hobbesian sovereign. The difficulty is to explain how this happens, and to distinguish the circumstances under which private provision of public goods succeeds from those under which it fails. To a greater extent than Jasay seems to think, economists and political scientists are tackling these questions. Much of the work of these disciplines might indeed be said to be drearily technical. But Jasay' s book gives us no reason to think that there is any easier way forward.


Robert Sugden is Professor of Economics at the University of East Anglia.

Copyright 1992 by the Institute for Humane Studies.

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