Constrained Plott equilibria, directional equilibria and global cycling sets

Abstract

Recent studies use two distinct approaches to study majority rule intransitivities. First, McKelvey (1976, 1979) and Cohen (1979) examine global cycling sets in multidimensional spaces. Second, Schofield (1977, 1978a, b) investigates local continuous cycling. Both approaches lead to the conclusion that cycling sets tend to be large. In this paper, these studies are related to each other and to the work of Matthews (1978, 1979) on undominated directions. Simple observations lead to a new and stronger result indicating the extreme pervasiveness of global cycling. The key observation is that global cycling is ubiquitous for the same reason that majority rule equilibria rarely exist, namely, that the distribution of voters is rarely symmetric enough.