A social welfare function based on dominating set relaxations

By relaxing the dominating set in several ways, we propose a social welfare function, which satisfies a number of attractive properties including anonymity (hence non-dictatorship), neutrality, strong Pareto (hence weak Pareto), and strong Gehrlein-stability (hence Smith set principle and Condorcet winner principle as well as Condorcet loser principle). It will return the majority relation when the majority relation is transitive, and thus it satisfies the property of independence of irrelevant alternatives in domains where the majority relation is guaranteed to be transitive. It runs in polynomial time. In tournaments, its winner belongs to the uncovered set (hence the top cycle set and Smith set as well as Schwartz set). In addition, in a tournament where the alternative number is not more than 4, its winner set is a subset, sometimes proper, of the Copeland winner set.