The uncovered set in spatial voting games |
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| Authors: | Scott L. Feld Bernard Grofman Richard Hartly Marc Kilgour Nicholas Miller with the assistance of Nicholas Noviello |
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| Affiliation: | (1) Department of Sociology, State University of New York at Stony Brook, 11794 Stony Brook, New York, USA;(2) School of Social Sciences, University of California, Irvine, 92717 Irvine, CA, USA;(3) General Electric Corporate Research and Development, Building KW Room C512, 12301 Schenectady, NY, USA;(4) Department of Mathematics, Wilfrid Laurier University, N2L 3C5 Waterloo, Ontario, Canada;(5) Department of Political Science, University of Maryland at Baltimore City, 5401 Wilkins Avenue, 21228 Catonsville, MD, USA;(6) School of Social Sciences, University of California, Irvine, 92717 Irvine, CA, USA |
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| Abstract: | ![]()
In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set. |
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