In Search of the Uncovered Set

This paper pursues a number of theoretical explorations and conjectures pertaining to the uncovered set in spatial voting games. It was stimulated by the article ‘‘The Uncovered Set and the Limits of Legislative Action’ ’ by W. T. Bianco, I. Jeliazkov, and I. Sened (2004, Political Analysis 12:256–78) that employed a grid-search computational algorithm for es-timating the size, shape, and location of the uncovered set, and it has been greatly facilitated by access to the CyberSenate spatial voting software being developed by Joseph Godfrey. I bring to light theoretical considerations that account for important features of the Bianco, Jeliazkov, and Sened results (e.g., the straight-line boundaries of uncovered sets displayed in some of their figures, the ‘‘unexpectedly large’ ’ uncovered sets displayed in other figures, and the apparent sensitivity of the location of uncovered sets to small shifts in the relative sizes of party caucuses) and present theoretical insights of more general relevance to spatial voting theory.