The Geometry of Voting

For any non collegial voting game, σ, there exists a stability dimension v*(σ), which can be readily computed. If the policy space has dimension no greater than v*(σ) then no local σ-cycles may exist, and under reasonable conditions, a σ-core must exist. It is shown here, that there exists an open set of profiles, V, in the c1 topology on smooth profiles on a manifold W of dimension at least v*(σ)+1, such that for each profile in v, there exist local σ-cycles and no σ-core