Computing and visualizing banks sets of dominance relations using relation algebra and RelView

In social choice theory the Banks set is a well-established choice set for tournaments that consists of the undominated elements of the maximal subtournaments. For non-complete dominance relations J. Duggan proposed three possibilities to modify it. We develop relation-algebraic specifications to compute the Banks set, Duggan’s modifications, and variants of them. All these specifications are algorithmic and can directly be translated into the programming language of the computer algebra system RelView. We show that the system is well suited for computing and visualizing the Banks set, its modifications, and the objects to be associated with them.