Liberal paradox, game equilibrium, and Gibbard optimum

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