Nash Consistent Representation of Constitutions: A Reaction to the Gibbard Paradox

The concept of an effectivity function is adopted as a formal model of a constitution. A game form models the actions available and permissible to individuals in a society. As a representation of the constitution such a game form should endow each group in society with the same power as it has under the constitution. Another desirable property is Nash consistency of the game form: whatever the individual preferences, the resulting game should be minimally stable in the sense of possessing a Nash equilibrium. A first main result of the paper is a characterization of all effectivity functions that have a Nash consistent representation for the case without special structure on the set of alternatives (social states). Next, a similar result is derived for the case where the set of alternatives is a topological space and the effectivity function is topological. As a special case, veto functions are considered. Further results concern Pareto optimality of Nash equilibrium outcomes.