Needing and Covering
نویسندگان
چکیده
In this paper, we define a binary relation for general collective choice situations, the needing relation, that captures one notion of dependence between alternatives with respect to inclusion in several popular solution concepts, including the top-cycle set, the uncovered set, the Banks set, and the minimal covering set. After defining the relation and relating it to a graph theoretical view of collective preference, we prove several results about the relation and provide a partial characterization of external stability of some tournament solution concepts. We then utilize the needing relation to define a property of tournament solution concepts, which we dub independence. Finally, the independence of several solution concepts is characterized.
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