BARGAINING FOR JUSTICE* RUSSELL HARDIN David Gauthier's Morals by Agreement1 presents a partial theory of distributive justice. It is partial because it applies only to the distribution of gains from joint endeavors, or what we may call the 'social surplus' from cooperation. This surplus is the benefit we receive from cooperation insofar as this is greater than what we might have produced through individual efforts without interaction with others. The central core of Gauthier's theory of distributive justice is his bargaining theory of 'minimax relative concession' o.r MRC. Whether his theory is compelling turns essentially on whether MRC is workable and compelling. It is this issue that I wish to address. Unfortunately, from what Gauthier has written about it, we cannot be fully confident that MRC is workable. The theory has in common with most formal bargaining theory that it is done entirely in utilities. In some contexts this can be risky because it masks too much of what is at issue. Formal bargaining theory is not about how to bargain but about what resolution of a bargaining problem rational bargainers should reach. It has been applied with compelling results to the problem of 'fair division', as for example, when you and I must decide how to divide the gift of cake that has been placed before us. One of the great strengths of Gauthier's verbal discussion of the problem of distributive justice, however, is his recognition that the distribution of free gifts is not an analogue of our problem. When we investigate distributive justice, we are not concerned with how to allocate manna from heaven, but with how to allocate what we have first produced. The latter problem is more difficult because it inherently involves incentive effects: we are individually apt to produce more the more we individually get of what we produce. My contribution to the whole social product will be small, and my fraction of my contribution will be negligible. If what I get is a specific fraction of the whole social product and if my costs of • This paper has benefited from discussions with many people, especially David Gauthier, James Buchanan, and others at the Bowling Green conference, and John Roemer. 1 David Gauthier, Morals b)' Aµeemmt (Oxford: Clarendon Press, 1986). (Henceforth, page number references to this book will be given parenthetically in the text.) 66 RUSSELL HARDIN BARGAINING FOR JUSTICE 67 contribution are significant,. then I would sooner not contribute and merely whole surplus but, practically, each would have to settle for less. The settle for my fraction of what everyone else contributes. Our problem, then, biggest concession one would make would be to settle for none of the gain; is to reward me directly for my contribution in order to secure it, and then the smallest would be to insist on the whole gain. A reasonable compromise to allocate to me my share of the remaining social product after each would be to have each bargainer settle for the same proportionate individual's contribution has been directly rewarded. This is the problem concession from full gain. Hence, relative concessions should be equal. When Gauthier sees as the central issue for a principle of distributive justice that there are more than two parties involved, equality of relative concessions is grounded in rational, self-interested calculation by all potential may not be possible or desirable, so that Gauthier stipulates that "an contributors and benefiters. outcome be selected only if the greatest or maximum relative concession it On this account the problem of distributive justice is the grandest of requires is as small as possible, or a minimum, that is, is no greater than the instances of the logic of collective action. It is not surprising, therefore, that maximum relative concession required by every other outcome" (A1A, Gauthier typically sees the issue as one of resolving Prisoner's Dilemma p.137). This is the principle of minimax relative concession, or MRC. interactions, because the Prisoner's Dilemma is an analogue of collective The core of Gauthier's theory is the claim that MRC provides the most action problems with perverse incentive effects that suggest that rational, compelling resolution of the problem of rationally, self-interestedly self-interested individuals will fail to cooperate for mutual benefit. 2 The accepting a specific allocation of the social · product. We need not here extraordinary value of Gauthier's theory, if it is compelling, is that it consider his arguments for why this particular bargaining theory - a variant potentially resolves all such problems. Given that such problems seemingly of a particular one of the many extant bargaining theories - is the natural abound, we must suppose that Gauthier's theory is wrong or that people choice of a ratio~al person. Rather, we need only consider whether MRC have simply failed to understand their rational self-interest in cooperation. can do the job set for it. There are many reasons to question whether MRC Perhaps even more impressively, we must suppose Gauthier has succeeded is an adequate principle for allocating the social product (whenever this in cracking a problem that many of the best social theorists of the past two term is used without modifier, it is assumed to be net of all individuals' millennia have recognized as central but have failed to crack. It is an contributions to it). One of the most transparent is that it fails Gauthier's audacious supposition. If it is correct, Gauthier's result is, philosophically, own demands in a problem that Gauthier himself analyzes for us. Another world-historical. Although it wouh.! be pleasing to see and praise a world­ is to see what is masked behind the concern with pure utilities for gains. historical move by a philosopher, I will argue that Gauthier's result is not Consider each of these in the context of the cooperative effort of Adelaide compelling, that the theory he offers does not work for even the partial and Ernest. problem of distributive justice that he addresses. To explicate and justify his theory, Gauthier presents many examples to show how it works and to say why its results are compelling. One of these problems is a cooperative .venture between Adelaide and Ernest. The MINIMAX RELATIVE CONCESSION venture is a variant of a mutual fund. Gauthier supposes that, for the range of their cooperation, "their utilities are linear with monetary values, so that The most that anyone could claim from a joint effort would be the whole we may give the payoffs in dollars" (A1A, p.137). Each contributes product minus the value of the contributions of other parties to it. The something to the project, which returns gains above the contributions. If least one would accept would be the value of one's own contribution to it. Adelaide were to receive all of the gains, she would get a value to her of What we have to divide, therefore, is the entire product of our joint effort $500. If Ernest were to receive all of the gains, he would get a value to him over and above our contributions to it or, again, the social product. A of $50. Under MRC Adelaide must concede $147 of her possible bargaining theory or a theory of distribution could allocate this net product maximum gain and Ernest must concede $15, so that the net payoffs to in any one of many ways. Gauthier supposes that rational bargainers would them are $353 and $35, respectively, with rounding off to the nearest propose to allocate it by agreeing on how much each would concede to the dollar. Adelaide's relative concession is 147 parts in 500 and Ernest's is 15 others in order to get them to cooperate. Ideally, each would want the parts in 50, so that their relative concessions are equal. Note how odd this result is. The total gain to Adelaide and Ernest, in i Mancur Olson, Jr., The L"gic of Colledive Action (Cambridge, MA: Harvard University Press, 1965); Russell Hardin, Collectittt Aaio11 (Baltimore, MD: Johns Hopkins University dollars, is only $388. If Adelaide had received all of the gain, she could Press for Resources for the Future, 1982). have paid Ernest considerably more than $35 while still having a net gain 68 RUSSELL HARDIN BARGAINING FOR JUSTICE 69 of more than $353 for herself. MRC seems to yield a perversely suboptimal contexts, of course, agreement of any kind is ruled out, so that MRC result that genuinely rational bargainers should be able to avoid. In the cannot be applied. actual world, bargaining without the possibility of side-payments in such Now let us go behind the allocation of net gains to see how they might contexts would be foolish. But Gauthier wants us to bargain cooperatively, have been produced. Suppose the cost of their joint venture was $250 and which is to say, with the possibility of relevant binding agreements, such as that Adelaide paid $200 and Ernest $50. (Gauthier simplifies his that which Adelaide and Ernest would want to make in order to net more discussion by assuming that their contributions are both $0 [MA, p.138].) each from the possible total payoff of $500.3 If Adelaide and Ernest bargain Let us follow Gauthier to calculate their relative concessions. He says: fully cooperatively, then the gain from their mutual effort should be $500, The relative magnitude of any concession may be expressed as the and each of them could claim to net this much at a maximum from the proportion its absolute magnitude bears to the absolute magnitude effort. In that case, they have identical MRC calculations, so that they get of a complete concession.