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Table of Contents
Intro; Preface; References; Contents; 1 Introduction; Abstract; Exercises; Answers to Exercises; References; 2 Voting Paradoxes; Abstract; 2.1 Simple Paradoxes; 2.1.1 The Condorcet Winner Paradox (Condorcet de 1785; Black 1958); 2.1.2 The Absolute Majority Winner Paradox; 2.1.3 The Condorcet Loser or Borda Paradox (Borda de 1784; Black 1958); 2.1.4 The Absolute Majority Loser Paradox; 2.1.5 The Pareto (or Dominated Candidate) Paradox (Fishburn 1974); 2.2 Conditional Paradoxes; 2.2.1 Additional Support (or Lack of Monotonicity or Negative Responsiveness) Paradox (Smith 1973; Fishburn 1974a
Fishburn and Brams 1983)2.2.2 Reinforcement (or Inconsistency or Multiple Districts) Paradox (Young 1974); 2.2.3 Truncation Paradox (Brams 1982; Fishburn and Brams 1983); 2.2.4 No-Show Paradox (Fishburn and Brams 1983; Ray 1986; Moulin 1988b; Holzman 1988/1989; Perez 1995); 2.2.5 Twin Paradox (Moulin 1988b); 2.2.6 Violation of the Subset Choice Condition (SCC) (Fishburn 1974b, c; 1977); 2.2.7 Preference Inversion Paradox; 2.2.8 Dependence on Order of Voting (DOV) Paradox (Farquharson 1969); Exercises; Answers to Exercises; References
3 Voting Procedures Designed to Elect a Single CandidateAbstract; 3.1 Non-Ranked Voting Procedures; 3.1.1 Plurality Voting (aka First Past the Post) Procedure; 3.1.2 Plurality with Runoff Voting Procedure; 3.1.3 Approval Voting (Brams and Fishburn 1978, 1983); 3.1.4 Successive Elimination (Farquharson 1969); 3.2 Ranked Voting Procedures that are not Condorcet-Consistent; 3.2.1 Borda's Count (Borda 1784; Black 1958); 3.2.2 Alternative Vote (aka Instant Runoff); 3.2.3 Coombs' Method (Coombs 1964, pp. 397-399; Straffin 1980; Coombs et al. 1984)
3.2.4 Bucklin's Method (Hoag and Hallett 1926, pp. 485-491 Tideman 2006, p. 203); 3.2.5 Range Voting (Smith 2000); 3.2.6 Majority Judgment (Balinski and Laraki 2007a, b, 2011); 3.3 Ranked Voting Procedures that are Condorcet-Consistent; 3.3.1 The Minimax Procedure; 3.3.2 Dodgson's Procedure (Black 1958, pp. 222-234; McLean and Urken, 1995, pp. 288-297); 3.3.3 Nanson's Method (Nanson 1883; McLean and Urken 1995, Ch. 14); 3.3.4 Copeland's Method (Copeland 1951); 3.3.5 Black's Method (Black 1958, p. 66); 3.3.6 Kemeny's Method (Kemeny 1959; Kemeny and Snell 1960
Young and Levenglick 1978 Young 1988, 1995); 3.3.7 Schwartz's Method (Schwartz 1972, 1986); 3.3.8 Young's Method (Young 1977); Exercises; Answers to Exercises; References; 4 The (In)Vulnerability of Non-Ranked Voting Procedures to Various Paradoxes; Abstract; 4.1 The (In)Vulnerability of the Plurality Voting Procedure to Various Paradoxes; 4.1.1 The Condorcet Winner, the Condorcet Loser, the Absolute Majority Loser, the Preference Inversion, and the SCC Paradoxes; 4.1.1.1 Example; 4.1.2 Absolute Majority Winner Paradox; 4.1.3 Pareto-Dominated Candidate Paradox
Fishburn and Brams 1983)2.2.2 Reinforcement (or Inconsistency or Multiple Districts) Paradox (Young 1974); 2.2.3 Truncation Paradox (Brams 1982; Fishburn and Brams 1983); 2.2.4 No-Show Paradox (Fishburn and Brams 1983; Ray 1986; Moulin 1988b; Holzman 1988/1989; Perez 1995); 2.2.5 Twin Paradox (Moulin 1988b); 2.2.6 Violation of the Subset Choice Condition (SCC) (Fishburn 1974b, c; 1977); 2.2.7 Preference Inversion Paradox; 2.2.8 Dependence on Order of Voting (DOV) Paradox (Farquharson 1969); Exercises; Answers to Exercises; References
3 Voting Procedures Designed to Elect a Single CandidateAbstract; 3.1 Non-Ranked Voting Procedures; 3.1.1 Plurality Voting (aka First Past the Post) Procedure; 3.1.2 Plurality with Runoff Voting Procedure; 3.1.3 Approval Voting (Brams and Fishburn 1978, 1983); 3.1.4 Successive Elimination (Farquharson 1969); 3.2 Ranked Voting Procedures that are not Condorcet-Consistent; 3.2.1 Borda's Count (Borda 1784; Black 1958); 3.2.2 Alternative Vote (aka Instant Runoff); 3.2.3 Coombs' Method (Coombs 1964, pp. 397-399; Straffin 1980; Coombs et al. 1984)
3.2.4 Bucklin's Method (Hoag and Hallett 1926, pp. 485-491 Tideman 2006, p. 203); 3.2.5 Range Voting (Smith 2000); 3.2.6 Majority Judgment (Balinski and Laraki 2007a, b, 2011); 3.3 Ranked Voting Procedures that are Condorcet-Consistent; 3.3.1 The Minimax Procedure; 3.3.2 Dodgson's Procedure (Black 1958, pp. 222-234; McLean and Urken, 1995, pp. 288-297); 3.3.3 Nanson's Method (Nanson 1883; McLean and Urken 1995, Ch. 14); 3.3.4 Copeland's Method (Copeland 1951); 3.3.5 Black's Method (Black 1958, p. 66); 3.3.6 Kemeny's Method (Kemeny 1959; Kemeny and Snell 1960
Young and Levenglick 1978 Young 1988, 1995); 3.3.7 Schwartz's Method (Schwartz 1972, 1986); 3.3.8 Young's Method (Young 1977); Exercises; Answers to Exercises; References; 4 The (In)Vulnerability of Non-Ranked Voting Procedures to Various Paradoxes; Abstract; 4.1 The (In)Vulnerability of the Plurality Voting Procedure to Various Paradoxes; 4.1.1 The Condorcet Winner, the Condorcet Loser, the Absolute Majority Loser, the Preference Inversion, and the SCC Paradoxes; 4.1.1.1 Example; 4.1.2 Absolute Majority Winner Paradox; 4.1.3 Pareto-Dominated Candidate Paradox