The Banks Set in Infinite Spaces

I provide a definition of the Banks set, or set of sophisticated voting outcomes, over an infinite policy space and when individual preferences are weak. I also show that the Banks set is a subset of one definition of the uncovered set, but not another. The interpretation of the Banks set in this setting differs from Banks’s original interpretation in the implicit role of the agenda setter. In addition, a characterization of the Banks set is provided for a three-player game of distributive politics. In this special setting, the Banks set and all definitions of the uncovered set have full measure over the space of alternatives.