Negative freedom and the liberal paradoxes

In their game-theoretic formulations, the liberal paradoxes of Amartya Sm and Alan Gibbard show a tension between freedom on the one hand, and Pareto optimality and stability on the other. This article examines what happens to the liberal paradoxes if a negative conception of freedom is used. Given a game-theoretic definition of negative freedom, it is shown, first, that the liberal paradoxes disappear in this new context: there are game forms in which individuals have a minimal amount of negative freedom and which guarantee the existence of Pareto-optimal and stable outcomes. Furthermore, if a game form gives each individual a maximal amount of negative freedom, the Pareto optimality of each stable outcome of the corresponding game is guaranteed. However, many games that provide such maximal negative freedom do not contain stable outcomes. We show that the liberal paradox may reappear in the mixed extension of such games.