Core Parties

In spatial voting games, the Condorcet winner is any policy or candidate that defeats all other policies or candidates in pairwise votes. However, what can we say about potential outcomes if there is no Condorcet winner? Let us define a set X as the set of feasible outcomes corresponding to vectors that denote the utility u of each player (ui, u2, u3,) to be a specific vector (i.e., point) in X. Assume that a coalition C prefers u to u if and only if ui > u,I for all individuals I in C. Define the coalition of individuals C to be effective for u in X if the members of C can coordinate their actions sufficiently to ensure that each member i of C receives a payoff of at least ui. Let v(C) denote the set of all utility n-tuples for which C is effective. Now we say that u dominates u if there exists at least one coalition that is effective for u and that prefers u to u. A cooperative game's core is then defined as the set of undominated elements of X.