Strong equilibrium outcomes of voting games are the generalized Condorcet winners

Abstract

We consider voting games induced by anonymous and top-unanimous social choice functions. The class of such social choice functions is quite broad, including every t-refinement of the Plurality Rule, Plurality with a Runoff, the Majoritarian Compromise and the Single Transferable Vote, i.e., any selection from either of these social choice rules which is obtained via tie-breaking among candidates according to any total order t on the set of alternatives. As announced in our title, the strong equilibrium outcomes of the voting games determined by such social choice functions turn out to be nothing but generalized Condorcet winners, namely the (n,q)-Condorcet winners. In the case of social choice functions (such as those just listed) which are furthermore top-majoritarian, they coincide with the classical Condorcet winners.