Classification theorem for smooth social choice on a manifold

Abstract

A classification theorem for voting rules on a smooth choice space W of dimension w is presented. It is shown that, for any non-collegial voting rule, σ, there exist integers v*(σ), w*(σ) (with v*(σ)<w*(σ)) such that 1.(i) structurally stable σ-voting cycles may always be constructed when w ⪴ v*(σ) + 1 2.(ii) a structurally stable σ-core (or voting equilibrium) may be constructed when w ⪴ v*(σ) − 1 Finally, it is shown that for an anonymous q-rule, a structurally stable core exists in dimension n−2/n−q, where n is the cardinality of the society.