Monotonicity Failures Afflicting Procedures for Electing a Single Candidate

In: SpringerBriefs in Economics

Abstract

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