Abstract
This chapter shows that the analysis of cooperative voting in any voting method has much to do with the underlying allocation of veto power to individuals and coalitions. As an effectivity function describes a particular allocation of power among agents and coalitions of agents, its main strategic feature is cooperative stability. The chapter focuses on stable effectivity functions, of which the main examples are the additive effectivity functions derived from the general voting by veto methods. The strong equilibrium is a very demanding concept that fails to exist in many usual normal form games. However, implementation by strong equilibrium is possible for a rich family of social choice correspondences. Behavioral justifications of the Nash equilibrium are not easy to provide. Traditional game theory views it both as a non-cooperative stability notion—when individual agents are myopic, that is, ignore the possible reactions by the other players to their own moves, and a cooperative concept, a Nash equilibrium outcome is an agreement self-enforced by mutual secrecy.
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