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, ⋆ I am grateful to David Austen-Smith, Kim Border, John Duggan, Matthew Jackson, Jonathan Katz, Bill Keech, Tom Palfrey, John Patty, Ken Shepsle, and especially to Richard McKelvey for their comments and advice. I would also like to thank two anonymous referees for their helpful suggestions. This paper is drawn from my 2003 Caltech dissertation. 2 Elizabeth Maggie Penn the Banks set and all definitions of the uncovered set have full measure over the space of alternatives.