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The (Stabilized) Nash Bargaining Solution as a Principle of Distributive Justice

  • MICHAEL MOEHLER (a1)
Abstract

It is argued that the Nash bargaining solution cannot serve as a principle of distributive justice because (i) it cannot secure stable cooperation in repeated interactions and (ii) it cannot capture our moral intuitions concerning distributive questions. In this article, I propose a solution to the first problem by amending the Nash bargaining solution so that it can maintain stable cooperation among rational bargainers. I call the resulting principle the stabilized Nash bargaining solution. The principle defends justice in the form ‘each according to her basic needs and above this level according to her relative bargaining power’. In response to the second problem, I argue that the stabilized Nash bargaining solution can serve as a principle of distributive justice in certain situations where moral reasoning is reduced to instrumental reasoning. In particular, I argue that rational individuals would choose the stabilized Nash bargaining solution in Rawls’ original position.

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1 See, for example, Rawls John, A Theory of Justice (Cambridge, 1971/1999), p. 116, and Sen Amartya, Collective Choice and Social Welfare (San Francisco, 1970), p. 121.

2 For the difference principle, see Rawls, A Theory of Justice, pp. 65–73, and Justice as Fairness – A Restatement, ed. Erin Kelly (Cambridge, 2001), pp. 42–3. For the average utility principle, see Harsanyi John, ‘Can the Maximin Principle Serve as a Basis for Morality? A Critique of John Rawls's Theory’, The American Political Science Review 69 (1975), pp. 594606.

3 See Rawls, Political Liberalism (New York, 1993), p. 19.

4 Rawls, Political Liberalism, p. 51.

5 See Rawls, A Theory of Justice, pp. 109–12, and Justice as Fairness – A Restatement, pp. 84–5.

6 See Rawls, A Theory of Justice, pp. 102–68.

7 Rawls, Justice as Fairness – A Restatement, pp. 81–2, italics added. For simplicity, I speak only of individuals in the following, and not of representatives of individuals or representatives of groups of individuals in Rawls’ original position.

8 The latest statement of the liberty principle and the fair equality of opportunity principle can be found in Rawls, Justice as Fairness – A Restatement, p. 42. Whether the individuals choose Rawls’ liberty principle and the fair equality of opportunity principle in the original position, or slightly different principles, is irrelevant for my argument that focuses exclusively on the domain of the difference principle.

9 The notion of a minimum standard of living is vague and can be defined in various ways. For the purpose of this article, I assume that the members of society come to an agreement on the determinants that define an individual's minimum standard of living and on a way to measure it. I return to this point in section VI.

10 See Nash John Jr., ‘The Bargaining Problem’, Econometrica 18 (1950), pp. 155–62, and ‘Two-Person Cooperative Games’, Econometrica 21 (1953), pp. 128–40. The individuals’ preferences are assumed to be represented by von Neumann–Morgenstern utility functions. In addition, I assume that, in our specific case, the conflicting parties accept the disagreement point as a basis for conflict resolution. I return to this assumption in section VI.

11 For further discussion of these axioms, see Luce R. Duncan and Raiffa Howard, Games and Decisions (New York, 1957), pp. 126–7.

12 The best-known bargaining solution that relies on interpersonal comparisons of utility is the egalitarian bargaining solution. See, in particular, Kalai Ehud, ‘Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons’, Econometrica 45 (1977), pp. 1623–30. Ken Binmore also defends such a proportional bargaining solution as an ethical solution concept in the context of his social contract theory. See Binmore, Game Theory and the Social Contract (Cambridge, 1994/1998), in particular, vol. 2, pp. 393–5. Other explicitly ethical bargaining solutions are defended by so-called arbitration models that specify bargaining outcomes that satisfy certain moral or fairness criteria. See, for example, Braithwaite Richard, Theory of Games as a Tool for the Moral Philosopher (Cambridge, 1955).

13 See Kalai Ehud and Smorodinsky Meir, ‘Other Solutions to Nash's Bargaining Problem’, Econometrica 43 (1975), pp. 513–18.

14 See Gauthier David, Morals by Agreement (Oxford, 1986), pp. 113–56.

15 See Roth Alvin, ‘An Impossibility Result Concerning n-Person Bargaining Games’, International Journal of Game Theory 8 (1979), pp. 129–32. In this context, see also Young H. Peyton, Equity: In Theory and Practice (Princeton, 1994), pp. 121–2, who argues that the Kalai–Smorodinsky solution is inconsistent in multi-party bargaining games.

16 See Zeuthen Frederik, Problems of Monopoly and Economic Warfare (London, 1930), ch. 4.

17 See Harsanyi, ‘Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hicks’, and Nash's Theories’, Econometrica 24 (1956), pp. 144–57, and Rational Behavior and Bargaining Equilibrium in Games and Social Situations (Cambridge, 1977), pp. 141–66.

18 See Rubinstein Ariel, ‘Perfect Equilibrium in a Bargaining Model’, Econometrica 50 (1982), pp. 97109. To be precise, Nash himself already presented a non-cooperative approach to his axiomatically derived bargaining solution in ‘Two-Person Cooperative Games’.

19 For further support of the Nash bargaining solution in this context, see, for example, Barry Brian, Theories of Justice (Berkeley, 1989), pp. 22–4; Binmore Ken, ‘Bargaining and Morality’, Rationality, Justice and the Social Contract, ed. Gauthier David and Sugden Robert (Ann Arbor, 1993), pp. 131–56, Game Theory and the Social Contract, vol. 1, pp. 80–4 and vol. 2, pp. 77–95, and Natural Justice (Oxford, 2005), pp. 25–7; and Skyrms Brian, Evolution of the Social Contract (Cambridge, 1996), p. 107. See also the later Gauthier who argues, in ‘Uniting Separate Persons’, in Rationality, Justice and the Social Contract, pp. 176–92, at pp. 176–9, that the real work of justifying his bargaining solution in the circumstances of the social contract is to show that it coincides with the Nash bargaining solution.

20 See Rawls, A Theory of Justice, pp. 12, 124, and 464, and Justice as Fairness – A Restatement, pp. 87–8.

21 See Harsanyi, ‘Can the Maximin Principle Serve as a Basis for Morality? A Critique of John Rawls's Theory’.

22 The later Rawls tries to make his argument for the difference principle less dependent on the use of the maximin rule in the original position. I think, however, without success. For this point, see Rawls, Justice as Fairness – A Restatement, p. 95, and my discussion in the following section.

23 See Rawls, Justice as Fairness – A Restatement, pp. 119–30.

24 See Rawls, Justice as Fairness – A Restatement, pp. 130 and 162.

25 Rawls, A Theory of Justice, p. 126.

26 For a more general discussion of this point, see Cohen G. A., Rescuing Justice and Equality (Cambridge, 2008), pp. 2786.

27 See Rawls, A Theory of Justice, pp. 134–5, and Justice as Fairness – A Restatement, pp. 97–104.

28 For an alternative decision-theoretic defense of the use of the maximin rule in Rawls’ original position, see Angner Erik, ‘Revisiting Rawls: A Theory of Justice in the Light of Levi's Theory of Decision’, Theoria 70 (2004), pp. 321.

29 For the device of the reflective equilibrium, see Rawls, A Theory of Justice, pp. 18–19.

30 For a similar point, see Gauthier, ‘Bargaining and Justice’, Social Philosophy and Policy 2 (1985), pp. 2947, at p. 44, and ‘Justice as Social Choice’, Morality, Reason, and Truth – New Essays on the Foundations of Ethics, ed. David Copp and David Zimmermann (Totowa, 1984), pp. 251–69, at p. 255.

31 Rawls is explicit that there are ‘no objective grounds in the initial situation for assuming that one has an equal chance of turning out to be anybody’ (A Theory of Justice, p. 144), and that the choice in the original position is not to be guided by probability considerations. Whether this assumption is plausible is an entirely different question that is not of concern here. For a discussion of this point, see in particular Binmore, Game Theory and the Social Contract, vol. 1, pp. 327–9. For further discussion of the use of the principle of insufficient reason in Rawls’ original position, see Rawls, A Theory of Justice, pp. 134–5 and pp. 144–50; Rawls, Justice as Fairness – A Restatement, p. 98; and Freeman Samuel, Rawls (New York, 2007), pp. 175–7. With regard to the use of the principle of insufficient reason, it is also interesting that Harsanyi himself argues later in, ‘Bayesian Decision Theory, Subjective and Objective Probabilities, and Acceptance of Empirical Hypotheses’, Synthese 57 (1983), pp. 341–65, at p. 352, that the principle ‘is open to the important logical objection that it attempts to draw a positive conclusion (that of equal probabilities) from mere ignorance (from absence of information favoring any specific outcome) – an attempt that cannot possibly succeed’.

32 Rawls’ theory of justice faces a similar problem with regard to determining the criteria that define the worst-off group in society. See Rawls, Justice as Fairness – A Restatement, pp. 57–61, for example.

33 See Nozick Robert, Anarchy, State, and Utopia (Oxford, 1974), pp. 153–60.

34 I think that Nozick's claim in Anarchy, State, and Utopia, p. 199, that Rawls’ original position rules out the choice of any historical principle of distributive justice is partly misguided. The individuals in Rawls’ original position do not know their specific holdings in real life, but they know that they will be endowed with certain holdings. As such, they must decide on the status of those holdings in the original position, although their decisions under the veil of ignorance are not allowed to be guided by moral considerations. The individuals may regard historical entitlements as irrelevant to their considerations in the original position, and consequently choose an end-state principle of distributive justice. Or, they may regard historical entitlements as relevant to their considerations in the original position, and consequently choose a historical principle of distributive justice, as in our case, which relies on the assumption that instrumental rationality combined with the ideal of individual utility maximization requires agents to defend their preferences in conflicts over the cooperative surplus at least as much as possible according to their actual capacities in real life. This requirement is not a moral assumption, but it allows the choice of a historical principle of distributive justice in Rawls’ original position.

35 The resulting form of the state, if the stabilized Nash bargaining solution is implemented as a principle of distributive justice, is best described as a minimal welfare state, in contrast to Rawls’ defense of a property-owning democracy and liberal socialism (see Rawls, Justice as Fairness – A Restatement, pp. 135–8), although further institutional arrangements may have to be made if Rawls’ liberty principle and the fair equality of opportunity principle are also implemented.

36 I am grateful to Richard Bradley, Mark LeBar, Stuart Rachels, Robert Sugden, Alex Voorhoeve, and the audiences of various conferences and seminars at which I presented earlier versions of this article for their helpful discussions and comments.

37 The stabilized starting point for the bargaining process reflects the utility levels that the individuals must at least reach in the short run in order to have an interest in stable long-term cooperation, which are the utility levels that reflect the individuals’ minimum standards of living.

38 If both individuals are below their subsistence levels when the conflict arises, then both parties must reach their minimum standards of living before the standard Nash bargaining solution is applied, assuming that the overall cooperative surplus permits it. If both individuals are below their subsistence levels when the conflict arises, and the overall cooperative surplus cannot bring both parties to their subsistence levels, then the conflict will be resolved according to the standard Nash bargaining solution.

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Utilitas
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