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Published 1995 | public
Journal Article

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.

Additional Information

© 1995 Elsevier Science B.V. Submitted May 1994; accepted September 1994. I would like to thank David Austen-Smith, Steve Landsburg, Richard McKelvey, John Nachbar, Andy Rutten, Norman Schofield, and two anonymous referees for numerous enlightening comments and suggestions. Financial support from the Sloan Foundation and the National Science Foundation is also gratefully acknowledged.

Additional details

August 22, 2023
October 18, 2023