The uncovered set and indifference in spatial models: A fuzzy set approach

The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.

[1]  Terry D. Clark,et al.  Applying Fuzzy Mathematics to Formal Models in Comparative Politics , 2008, Studies in Fuzziness and Soft Computing.

[2]  D. Green,et al.  Pathologies of Rational Choice Theory: A Critique of Applications in Political Science , 1994 .

[3]  Thomas Bräuninger.  Stability in Spatial Voting Games with Restricted Preference Maximizing , 2007 .

[4]  Kenji Yoshino,et al.  Covering , 1912, The Indian medical gazette.

[5]  David H. Koehler.  Convergence and Restricted Preference Maximizing under Simple Majority Rule: Results from a Computer Simulation of Committee Choice in Two-Dimensional Space , 2001, American Political Science Review.

[6]  Barry R. Weingast,et al.  Uncovered Sets and Sophisticated Voting Outcomes with Implications for Agenda Institutions , 1984 .

[7]  J. Bezdek,et al.  A fuzzy relation space for group decision theory , 1978 .

[8]  J. Kacprzyk,et al.  On fuzzy tournaments and their solution concepts in group decision making , 1991 .

[9]  C. Tovey.  The Instability of Instability , 1991 .

[10]  H. Nurmi.  Approaches to collective decision making with fuzzy preference relations , 1981 .

[11]  Elizabeth Maggie Penn.  Alternate Definitions of the Uncovered Set and Their Implications , 2006, Soc. Choice Welf..

[12]  J. Kacprzyk,et al.  Group decision making and consensus under fuzzy preferences and fuzzy majority , 1992 .

[13]  Janusz Kacprzyk,et al.  FUZZY SETS IN POLITICAL SCIENCE: AN OVERVIEW , 2007 .

[14]  J. Bezdek,et al.  Fuzzy relation spaces for group decision theory: An application , 1979 .

[15]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .

[16]  Charles R. Plott,et al.  A Notion of Equilibrium and Its Possibility Under Majority Rule , 1967 .

[17]  Michel Le Breton,et al.  Gillies and Miller's Subrelations of a Relation over an Infinite Set of Alternatives: General Results and Applications to Voting Games , 1992 .

[18]  Georges Bordes.  On the possibility of reasonable consistent majoritarian choice: Some positive results , 1983 .

[19]  Nicholas R. Miller.  In Search of the Uncovered Set , 2007, Political Analysis.

[20]  J. Kacprzyk,et al.  A ‘soft’ measure of consensus in the setting of partial (fuzzy) preferences , 1988 .

[21]  H. Nurmi.  A fuzzy solution to a majority voting game , 1981 .

[22]  J. Blin.  Fuzzy Relations in Group Decision Theory , 1974 .

[23]  B. Grofman,et al.  Why so much stability? Research note Partial single-peakednes s: An extension and clarification , 1986 .

[24]  Nicholas R. Miller.  A New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches to the Theory of Voting , 1980 .

[25]  Richard D. McKelvey,et al.  Covering, Dominance, and Institution Free Properties of Social Choice , 1986 .

[26]  James M. Enelow,et al.  On Plott's pairwise symmetry condition for majority rule equilibrium , 1983 .

[27]  J. Mordeson,et al.  THE EXISTENCE OF A MAJORITY RULE MAXIMAL SET IN ARBITRARY n-DIMENSIONAL SPATIAL MODELS , 2010 .

[28]  R. McKelvey.  Intransitivities in multidimensional voting models and some implications for agenda control , 1976 .

[29]  Siddhartha Bandyopadhyay.  Positive Political Theory II: Strategy and Structure. , 2006 .

[30]  Joseph Greenberg,et al.  CONSISTENT MAJORITY RULES OVER COMPACT SETS OF ALTERNATIVES , 1979 .

[31]  Judith Sloss,et al.  Stable outcomes in majority rule voting games , 1973 .

[32]  R. McKelvey.  General Conditions for Global Intransitivities in Formal Voting Models , 1979 .

[33]  William V. Gehrlein,et al.  Condorcet efficiency: A preference for indifference , 2001, Soc. Choice Welf..