A Set-Theoretical Comparison of C2 Social Choice Correspondences

Given the choice sets produced by a pair of Condorcet social choice correspondences, the following interesting questions arise. Does one of these sets always contain the other? If not, do they always intersect or, on the contrary, can they have an empty intersection? Laffond, Laslier, and Le Breton (1995) answer these questions for Condorcet social choice correspondences based exclusively on the simple majority relation, called C1 choice correspondences by Fishburn(1977). In the present paper, we conduct the same task for five Condorcet choice correspondences that require the size of the majorities to operate. These are called C2. The first two are the Kemeny and the Simpson-Kramer minmax rules. The other three are closely related to the solution of the plurality version of an electoral competition game involving two political parties. They select the set of weakly undominated strategies, a new minimal covering set and the support of the unique Nash equilibrium in mixed strategies of the electoral game. We also study the inclusionédisjunction relations between these five C2 choice correspondences and three of type C1, namely the top cycle, the uncovered set and the usual minimal covering set. The comparison is also done with the Borda rule.