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Liberal paradox, game equilibrium, and Gibbard optimum

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  • Friedrich Breyer
  • Roy Gardner

Abstract

Our analysis of a game-theoretic model of liberal rights had two main purposes: First, we gave a characterization of Gibbard's solution to the liberal paradox in terms of a game equilibrium. Secondly, we asked for preference restrictions that can guarantee the existence of a Pareto-optimal equilibrium in this ‘game of liberalism’. As one of our main results it turned out that voluntary cooperation between players does not by itself eliminate the possible occurrence of the liberal paradox if this is, in the cooperative context, defined as the emptiness of the core. Rather, we derived a sufficient condition that guaranteed a non-empty core of the cooperative game as well as a Pareto-optimal Nash equilibrium in the non-cooperative game: At least n — 1 of the n players must deem their own issue more important than all the other issues taken together. However, several important questions remain open. First, the relationship between Gibbard's social choice function f* and Arrow's famous conditions (1963, Chap. 3) has not been investigated. Although f* satisfies nondictatorship and the Pareto condition, it is likely that it fails both collective rationality and the independence condition. Finally, there is the question of whether other familiar SCF's, e.g. Condorcet's rule or Borda's rule, agree with f*. In so far as they do not, credence is lent to the view that certain aspects of a person's life are not to be put to a vote. This also makes libertarian antipathy to majority rule more understandable. Copyright Martinus Nijhoff Publishers bv 1980

Suggested Citation

  • Friedrich Breyer & Roy Gardner, 1980. "Liberal paradox, game equilibrium, and Gibbard optimum," Public Choice, Springer, vol. 35(4), pages 469-481, January.
    • Handle: RePEc:kap:pubcho:v:35:y:1980:i:4:p:469-481
    DOI: 10.1007/BF00128124
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    References listed on IDEAS

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    1. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
    2. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
    3. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-157, Jan.-Feb..
    4. Julian H. Blau, 1975. "Liberal Values and Independence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 395-401.
    5. John Aldrich, 1977. "The dilemma of a paretian liberal: Some consequences of Sen's theorem," Public Choice, Springer, vol. 30(1), pages 1-21, June.
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    Cited by:

    1. Christian Seidl, 1986. "The impossibility of nondictatorial tolerance," Journal of Economics, Springer, vol. 46(1), pages 211-225, December.
    2. Wulf Gaertner, 1986. "Pareto, interdependent rights exercising and strategic behaviour," Journal of Economics, Springer, vol. 5(1), pages 79-98, December.
    3. Ruvin Gekker, 1991. "On the impossibility of an envy-free Paretian liberal," Journal of Economics, Springer, vol. 53(1), pages 75-82, February.
    4. Ruvin Gekker, 1992. "On the strategic inconsistency of the meta-rights approach," Journal of Economics, Springer, vol. 55(3), pages 265-275, October.

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