Winners, blockers, and the status quo: Simple collective decision games and the core

3. Summary

This essay considers a general class of collective decision problems that may be represented as simple collective decision games. This analysis departs from the emphasis of the earlier literature on simple cooperative games by giving special attention to situations in which blocking coalitions are possible. We define a procedure for constructing the core of such games. We establish results demonstrating that, in simple games in which blocking coalitions are possible, the relative attractiveness of the no-decision or status quo outcome delimits the core. We prove theorems specifying necessary and sufficient conditions for any simple collective decision game to possess a nonempty core and for the status quo to belong to the core. The last theorem in this essay has special significance for solution theory about simple collective decision games. Any point in the core has a claim for stability if that point somehow becomes the tentative outcome of negotiations. But, mathematically, the core is a static equilibrium concept that, as such, does not specify a process leading to any feasible alternative as the tentative outcome. However, the status quo is the natural starting point of negotiations in collective decision making. Therefore, one can make a special claim for the stability of the status quo if it belongs to the core.