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Uniqueness and symmetry in bargaining theories of justice

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Abstract

For contractarians, justice is the result of a rational bargain. The goal is to show that the rules of justice are consistent with rationality. The two most important bargaining theories of justice are David Gauthier’s and those that use the Nash’s bargaining solution. I argue that both of these approaches are fatally undermined by their reliance on a symmetry condition. Symmetry is a substantive constraint, not an implication of rationality. I argue that using symmetry to generate uniqueness undermines the goal of bargaining theories of justice.

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Notes

  1. David Gauthier’s bargaining solution, minimax relative concession, is a variant of the Kalai-Smorodinsky solution (1975).

  2. Those include, for instance, Ken Binmore (1994) and Ryan Muldoon (2011a, b). Michael Moehler has defended a variant of the Nash bargaining solution, what he calls that stabilized Nash Bargaining solution (2010). H. Peyton Young also defends the Nash bargaining solution as being the most equitable bargaining solution (1995, p. 129).

  3. For a discussion of the importance of this earlier work to his later collaborative work with John von Neumann see: (Morgenstern 1976, p. 806; Innocenti 1995).

  4. Specifically, they modeled it as a form of “matching pennies.” The normal form of the game is below:

  5. Binmore also uses the language of twins in his discussion of the “paradox of the twins” and the “symmetry fallacy” (1994, pp. 203–256).

  6. In general, Rubinstein has shown that the Nash bargaining problem can be represented as a non-cooperative game. The basic idea that I am taking from Rubinstein is that solutions to bargaining problems can often be represented as equilibrium selection problems in non-cooperative games. Nash makes a different point in his 1953 article, but it is instructive that he also models one version of the bargaining problem as a multi-stage threat game.

  7. For Gauthier, the benefits of some system of constraint arise because of the probability of “market failures” in the use of individual reason that lead to prisoner’s dilemma like situations (1986, pp. 84–85).

  8. Consider the ultimatum game or the Nash demand game where every matching solution is a Nash equilibrium.

  9. Of course, Rawls claimed that the difference principle is not the result of bargaining in the traditional sense. This is partly because choice from behind the veil of ignorance is the choice of one person. He continues to use the language of “parties” left over from earlier formulations, however. In Sect. 3 of Theory, he claims “the principles of justice are the result of a fair agreement or bargain” (Rawls 1999, p. 11).

  10. This solution is similar in some ways to the correlated equilibrium solution that Herbert Gintis, following Robert Aumann, has proposed to solve similar indeterminacy problems in another context. Gintis introduces the solution concept to solve certain problems that arise when common knowledge does not obtain and it is appropriate in his context, but is inappropriate here (2009, 2010).

  11. Harsanyi is explicit about this (1982, p. 49) and Rawls makes it clear he is relying on symmetry in Political Liberalism (1996, p. 106).

  12. I thank an anonymous referee for alerting me to this point.

  13. This is exactly the kind of justification that Binmore makes to defend the evolutionary salience of fair social contracts in Natural Justice (Binmore 2005).

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Acknowledgments

Special thanks are due to Jerry Gaus and David Schmidtz for their helpful comments on earlier versions of this paper. I would also like to thank Steve Wall, Uriah Kriegel, David Copp, Chris Morris, Ryan Muldoon, Chris Freiman, Kevin Vallier, Keith Hankins, Danny Shahar, Chad Van Schoelandt, Victor Kumar, Michael Bukoski, Bill Glod, Mark Budolfson, and an anonymous referee for comments on earlier versions of this paper.

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Thrasher, J. Uniqueness and symmetry in bargaining theories of justice. Philos Stud 167, 683–699 (2014). https://doi.org/10.1007/s11098-013-0121-y

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