Designing Better Voting and Fair-Division Procedures
Buch, Englisch, 390 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 662 g
ISBN: 978-0-691-13321-8
Verlag: Princeton University Press
Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.
Autoren/Hrsg.
Fachgebiete
- Sozialwissenschaften Politikwissenschaft Politische Systeme Wahlen und Volksabstimmungen
- Sozialwissenschaften Politikwissenschaft Politische Kultur Politische Kommunikation und Partizipation
- Sozialwissenschaften Soziologie | Soziale Arbeit Spezielle Soziologie Freizeitsoziologie, Konsumsoziologie, Alltagssoziologie, Populärkultur
- Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
- Mathematik | Informatik Mathematik Operations Research Spieltheorie
Weitere Infos & Material
Preface xiii
PART 1. VOTING PROCEDURES 1
Chapter 1: Electing a Single Winner: Approval Voting in Practice 3
1.1. Introduction 3
1.2. Background 6
1.3. Early History 8
1.4. The Adoption Decisions in the Societies 10
1.5. Does AV Make a Difference? 14
1.6. Does AV Elect the Lowest Common Denominator? 16
1.7. Is Voting Ideological? 18
1.8. Summary and Conclusions 21
Chapter 2: Electing a Single Winner: Approval Voting in Theory 23
2.1. Introduction 23
2.2. Preferences and Strategies under AV 25
2.3. Election Outcomes under AV and Other Voting Systems 26
2.4. Stability of Election Outcomes 37
2.5. Summary and Conclusions 42
Appendix 43
Chapter 3: Electing a Single Winner: Combining Approval and Preference 46
3.1. Introduction 46
3.2. Definitions and Assumptions 48
3.3. Preference Approval Voting (PAV) 49
3.4. Fallback Voting (FV) 52
3.5. Monotonicity of PAV and FV 56
3.6. Nash Equilibria under PAV and FV 58
3.7. The Effects of Polls in 3-Candidate Elections 61
3.8. Summary and Conclusions 66
Chapter 4: Electing Multiple Winners: Constrained Approval Voting 69
4.1. Introduction 69
4.2. Background 70
4.3. Controlled Roundings 72
4.4. Further Narrowing: The Search May Be Futile 75
4.5. Constrained Approval Voting (CAV) 80
4.6. Unconstraining Votes: Two Alternatives to CAV 82
4.7. Summary and Conclusions 87
Chapter 5: Electing Multiple Winners: The Minimax Procedure 89
5.1. Introduction 89
5.2. Minisum and Minimax Outcomes 91
5.3. Minimax versus Minisum Outcomes: They May Be Antipodes 97
5.4. Endogenous versus Restricted Outcomes 101
5.5. Manipulability 103
5.6. The Game Theory Society Election 105
5.7. Summary and Conclusions 108
Appendix 109
Chapter 6: Electing Multiple Winners:
Minimizing Misrepresentation 112
6.1. Introduction 112
6.2. Obstacles to the Implementation of Proportional Representation (PR) 113
6.3. Integer Programming 115
6.4. Monroe?s System 116
6.5. Assigning More than One Candidate to a Voter 119
6.6. Approval Voting 121
6.7. Fractional Assignments 123
6.8. Noninteger k 125
6.9. The Chamberlin-Courant System 126
6.10. Tullock?s System 127
6.11. Weighted Voting 129
6.12. Nonmanipulability 130
6.13. Representativeness 131
6.14. Hierarchical PR 133
6.15. Summary and Conclusions 136
Appendixes 138
Chapter 7: Selecting Winners in Multiple Elections 143
7.1. Introduction 143
7.2. Referendum Voting: An Illustration of the Paradox of Multiple Elections 145
7.3. The Coherence of Support for Winning Combinations 149
7.4. Empirical Cases 155
7.5. Relationship to the Condorcet Paradox 160
7.6. Normative Questions and Democratic Political Theory 165
7.7. Yes-No Voting 167
7.8. Summary and Conclusions 169
PART 2. FAIR-DIVISION PROCEDURES 171
Chapter 8: Selecting a Governing Coalition in a Parliament 173
8.1. Introduction 173
8.2. Notation and Definitions 176
8.3. The Fallback (FB) and Build-Up (BU) Processes 177
8.4. The Manipulability of FB and BU 181
8.5. Properties of Stable Coalitions 182
8.6. The Probability of Stable Coalitions 186
8.7. The Formation of Majorities in the U.S. Supreme Court 189
8.8. Summary and Conclusions 193
Appendix 195
Chapter 9: Allocating Cabinet Ministries in a Parliament 199
9.1. Introduction 199
9.2. Apportionment Methods and Sequencing 202
9.3. Sophisticated Choices 206
9.4. The Twin Problems of Nonmonotonicity and Pareto-Nonoptimality 209
9.5. Possible Solutions: Trading and Different Sequencing 214
9.6. A 2-Party Mechanism 215
9.7. Order of Choice and Equitability 218
9.8. Summary and Conclusions 220
Appendix 221
Chapter 10: Allocating Indivisible Goods: Help the Worst-Off or Avoid Envy? 224
10.1. Introduction 224
10.2. Maximin and Borda Maximin Allocations 227
10.3. Characteriz
