A social welfare function based on dominating set relaxations
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Fujun Hou
Apr 23, 2025, 9:58:21 AMApr 23
to Online Social Choice and Welfare Forum
Dear Colleagues,
Greetings! The following linkage points to a new social welfare function:
Greetings! The following linkage points to a new social welfare function:
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A social welfare function based on dominating set relaxations
ABSTRACT
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.
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.
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