Monotonicity failures afflicting procedures for electing a single candidate

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). Contents: 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. Contents: 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. Contents: 3.1 Smith's (1973) Theorem3.2 Fishburn's (1982) Theorems; 3.3 Moulin's (1988) and Pérez's (2001) Theorems; 3.4 Saari's (1989) Results; 3.5 Muller and Satterthwaite (1977) Theorem; References; 4 Five Voting Rules Susceptible to Types of Monotonicity Failure Under Both Fixed and Variable Electorates; Abstract; 4.1 Introduction; 4.2 Types of Monotonicity Failure of the Plurality with Runoff Method Under Fixed Electorates; 4.2.1 An Initial Situation with a Condorcet Winner; 4.2.1.1 Upward Monotonicity Failure-Dynamic Voters Better Off [UB]. Contents: 4.2.1.2 Upward Monotonicity Failure-Dynamic Voters Worse Off [UW]4.2.1.3 Downward Monotonicity Failure-Dynamic Voters Better Off [DB]; 4.2.1.4 Impossibility: Downward Monotonicity Failure-Dynamic Voters Worse Off [DW]; 4.2.2 An Initial Situation with a Top Cycle; 4.2.2.1 Upward Monotonicity Failure-Dynamic Voters Better Off [UB]; 4.2.2.2 Upward Monotonicity Failure-Dynamic Voters Worse Off [UW]; 4.2.2.3 Downward Monotonicity Failure-Dynamic Voters Better Off [DB]; 4.3 Types of Monotonicity Failure of the Alternative Vote Method Under Fixed Electorates. Identifier: ISBN 9783319510613 (electronic bk.); ISBN 3319510614 (electronic bk.) 10.1007 978-3-319-51061-3 doi; BNB GBB8N7257; System number: 019164705