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"Rational Choice Theory in Political Decision Making" published on by Oxford University Press.

Preface -- Acknowledgements -- List of Figures -- List of Tables -- Fuzzy Social Choice -- 1.1 The Purpose and Plan of the Book -- 1.2 General Concepts -- 1.2.1 Sets -- 1.2.2 Subsets -- 1.2.3 Relations -- 1.2.4 Fuzzy Intersection and Union -- 1.2.5 Residuum -- References -- Classical Social Choice Theorems -- 2.1 Arrows Theorem -- 2.2 Discussion -- 2.3 Gibbard-Sattherthwaite Theorem -- 2.4 The Median Voter Theorem -- 2.5 The Maximal Set -- References -- Rationality of Fuzzy Preferences -- 3.1 The Structure of Fuzzy Preference Relations -- 3.2 Consistency of Fuzzy Preferences and the Fuzzy Maximal Set -- 3.3 Empirical Application I: Deriving an FWPR from a Fuzzy Preference Function -- References -- Arrow and the Aggregation of Fuzzy Preferences -- 4.1 Fuzzifying Arrow's Conditions -- 4.1.1 Transitivity -- 4.1.2 Weak Paretianism -- 4.1.3 Independence of Irrelevant Alternatives -- 4.1.4 Dictatorship -- 4.2 Making and Breaking Arrow's Theorem -- 4.3 Empirical Application II: The Spatial Model and Fuzzy Aggregation -- References -- Characteristics of Strategy-Proof Fuzzy Social Choice -- 5.1 Fuzzy Choice and Manipulation -- 5.2 Fuzzy Social Choice: Definitions and Concepts -- 5.2.1 Fuzzifying ASB II -- 5.2.2 Relaxing the Conditions of Abdelaziz et. al. -- 5.3 Findings -- 5.4 Implications for the Spatial Model -- 5.5 Conclusions -- References -- Fuzzy Black's Median Voter Theorem -- 6.1 The Structure of Fuzzy Rules and Strict Preference -- 6.2 Basic Definitions and Concepts -- 6.3 New and Old Fuzzy Voting Rules -- 6.4 Single-Peaked Preferences and the Maximal Set -- 6.5 Extending Black's Median Voter Theorem -- 6.6 An Application -- 6.7 Conclusions and Spatial Models -- References -- Representing Thick Indifference in Spatial Models -- 7.1 Stability and Thick Indifference in Individual Preferences

AbstractDuncan Black, like Adam Smith before him, was trained at, and taught at, the University of Glasgow. Like Smith, Black followed the Enlightenment in appreciating the importance of theory and of its empirical applications. Black sought to apply the ideas of a schedule of preferences and a conception of equilibrium, to politics, as Smith had done in economics. Black believed that his median voter theorem could generalize to a theory of politics, much as Smith's contributions did for market economics. Black did not complete that generalization, but William Riker did offer a theory of institutional politics, designed to complete Black's project.

Contents -- 1 Non-monotonic Voting Methods: An Overview -- Abstract -- 1.1 Introduction -- 1.2 Types of Monotonicity Failure -- 1.3 The Plan of the Book -- References -- 2 Descriptions of the Voting Methods to Be Analyzed -- Abstract -- 2.1 Introduction -- 2.2 Five Voting Methods Susceptible to Types of Monotonicity Failure Under Both Fixed and Variable Electorates -- 2.2.1 Plurality with Runoff (P-R) -- 2.2.2 Alternative Vote (AV -- aka Instant Runoff Voting -- Ranked Choice Voting) -- 2.2.3 The Coombs Method (Cf. Coombs 1964, pp. 397-399 -- Straffin 1980 -- Coombs et al. 1984) -- 2.2.4 The Dodgson Method (Cf. Black 1958, pp. 222-234 -- McLean and Urken 1995, pp. 288-297) -- 2.2.5 The Nanson Method (Cf. Nanson 1883 -- McLean and Urken 1995, Chap. 14) -- 2.3 Eight Voting Methods Susceptible to Types of Monotonicity Failure Under Variable Electorates -- 2.3.1 Successive Elimination (Cf. Farquharson 1969) -- 2.3.2 Bucklin's Method (Cf. Hoag and Hallett 1926, pp. 485-491 -- Tideman 2006, p. 203) -- 2.3.3 Majority Judgment (Cf. Balinski and Laraki 2007a, b, 2010) -- 2.3.4 Copeland's Method (Copeland 1951) -- 2.3.5 Black's Method (Black 1958, p. 66) -- 2.3.6 Kemeny's Method (Kemeny 1959 -- Kemeny and Snell 1960 -- Young and Levenglick 1978 -- Young 1988, 1995) -- 2.3.7 Schwartz's Method (Schwartz 1972, 1986) -- 2.3.8 Young's Method (Young 1977) -- 2.4 Five Main Procedures that Are not Susceptible to Any Monotonicity Failure -- 2.4.1 Plurality (or First Past the Post) Voting Procedure -- 2.4.2 Approval Voting (Brams and Fishburn 1978, 1983) -- 2.4.3 Borda's Count (Cf. de Borda 1784 -- Black 1958 -- McLean and Urken 1995, pp. 83-89) -- 2.4.4 Range Voting (Smith 2000) -- 2.4.5 The Minmax Procedure -- References -- 3 Some Theoretical Results on Monotonicity-Related Properties of Voting Rules -- Abstract -- 3.1 Smith's (1973) Theorem