Social choice and electoral competition in the general spatial model

This paper extends the theory of the core, the uncovered set, and the related undominated set to a general set of alternatives and an arbitrary measure space of voters. We investigate the properties of social preferences generated by simple games, we extend results on generic emptiness of the core, we prove the general nonemptiness of the uncovered and undominated sets, and we prove the upper hemicontinuity of these correspondences when the voters’ preferences are such that the core is nonempty and externally stable. Finally, we give conditions under which the undominated set is lower hemicontinuous. Jeff Banks passed away on December 21, 2000. The second and third authors wish to express their respect and admiration for Jeff as a colleague and dear friend. We will miss him. We are grateful for discussions with Kim Border, Mark Fey, Cesar Martinelli, Nicholas Miller, and Norman Schofield. We also thank a referee for helpful comments. Support from the National Science Foundation, grant number SES-0213738, is gratefully acknowledged.