Singularity theory and core existence in the spatial model

When the dimension of the outcome space in a voting game is sufficiently high, a core outcome will fail to exist for almost all utility profiles. Previous work by Schofield and McKelvey has identified critical dimensions for this generic non-existence, employing results on singularities of mappings and transversal intersections. In this paper we demonstrate that their proofs are incorrect, and determine the right dimensions implied by their singularity approach.