Simeone / Pukelsheim Mathematics and Democracy

Recent Advances in Voting Systems and Collective Choice
2006
ISBN: 978-3-540-35605-9
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 256 Seiten

Reihe: Studies in Choice and Welfare

In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

Autoren/Hrsg.

Simeone, Bruno

Pukelsheim, Friedrich

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;The Erice Decalogue;11
4;Power Indices Taking into Account Agents’ Preferences;13
4.1;1. Introduction;13
4.2;2. Main Notions;15
4.3;3. Ordinal Indices;16
4.4;4. Cardinal Indices;21
4.5;5. Evaluation for Russian Parliament;24
4.6;6. Axiomatic Construction of a Cardinal Intensity Function;25
4.7;7. Axioms for Power Indices;26
4.8;8. Concluding Remarks;28
4.9;Acknowledgments;28
4.10;References;29
5;The Sunfish Against the Octopus: Opposing Compactness to Gerrymandering;31
5.1;1. Introduction;31
5.2;2. A Combinatorial Gerrymandering Model;32
5.3;3. Theoretical Results on Grid Graphs;37
5.4;4. Experimental Results on Real-Life Test Problems;45
5.4.1;4.1 The Model and the Database;46
5.4.2;4.2 Districting Criteria and Local Search Algorithm;46
5.4.3;4.3 Experimental Plan and Results;50
5.5;References;53
6;Apportionment: Uni- and Bi-Dimensional;54
6.1;1. Introduction;54
6.2;2. Vector Apportionment: a Primer;54
6.3;3. From Divisions Between Two to Divisions Among All in Uni-Dimensional Apportionment;57
6.4;4. Matrix Apportionment: a Primer;59
6.5;5. From Divisions Between Two to Divisions Among All in Bi-Dimensional Apportionment;61
6.6;Acknowledgements;63
6.7;References;63
7;Minimum Total Deviation Apportionments;65
7.1;1. Introduction;65
7.2;2. Preliminaries;66
7.3;3. Minimum Total Deviation Apportionment;69
7.4;4. A Multiplicity of Minima;70
7.5;5. Bias;72
7.6;6. Alabama Paradox;73
7.7;7. Conclusion;74
7.8;References;74
8;Comparison of Electoral Systems: Simulative and Game Theoretic Approaches;75
8.1;1. Introduction;75
8.2;2. The Choice of the Optimal Electoral System;76
8.3;3. An Example;78
8.4;4. The Role of Power;79
8.5;5. Concluding Remarks;85
8.6;Appendix A - The Simulation Program;85
8.7;Appendix B - The Indices Employed;86
8.7.1;Index of Representativeness,;86
8.7.2;Index of Governability,;87
8.8;Appendix C - A Short Description of the Electoral Systems;88
8.9;Final Note;89
8.10;Acknowledgments;90
8.11;References;90
9;How to Elect a Representative Committee Using Approval Balloting;92
9.1;Introduction;92
9.2;1. Terminology and Notation;93
9.3;2. Minisum and Minimax Criteria;94
9.4;3. Weighted Distances;98
9.5;4. Conclusions;103
9.6;References;104
10;On Some Distance Aspects in Social Choice Theory;105
10.1;1. Introduction;105
10.2;2. Formal Framework;106
10.3;3. Choice Functions Versus Binary Relations;107
10.4;4. Distance Functions;110
10.5;5. Summary;112
10.6;Acknowledgements;112
10.7;References;112
11;Algorithms for Biproportional Apportionment;113
11.1;1. Introduction;113
11.2;2. Algorithms;115
11.2.1;2.1 Alternating Scaling Algorithm (AS);116
11.2.2;2.2 Tie-and-Transfer (TT);117
11.3;3. Properties and Data;118
11.4;4. Hybrid Algorithm;120
11.5;Acknowledgments;122
11.6;References;124
12;Distance from Consensus: A Theme and Variations;125
12.1;Introduction;125
12.2;1. The Methods;126
12.3;2. Consensus States and Metrics;129
12.4;3. Outranking and Tournament Matrices;133
12.5;4. Metrics Based on the Elimination of Candidates;135
12.6;5. Two More Systems;137
12.7;6. Conclusion;139
12.8;References;139
13;A Strategic Problem in Approval Voting;141
13.1;1. Introduction;141
13.2;2. Approval Voting in the First Four Presidential Elections;143
13.3;3. Generalizing from the Election of 1800;149
13.4;4. Conclusion;157
13.5;References;157
14;The Italian Bug: A Flawed Procedure for Bi-Proportional Seat Allocation;159
14.1;1. Introduction;159
14.2;2. Where the Italian System Fails;161
14.3;3. Electoral Paradoxes;162
14.4;4. Tackling the Italian Electoral Problem;168
14.5;5. Drawing Some Conclusions;171
14.6;Acknowledgments;172
14.7;References;172
15;Current Issues of Apportionment Methods;174
15.1;1. Introduction;174
15.2;2. A Gentle Majority Clause;175
15.3;3. Direct-Seat Restricted Methods;176
15.4;4. Biproportional Methods;179
15.5;References;182
16;A Gentle Majority Clause for the Apportionment of Committee Seats;184
16.1;1. Itio in Partes;184
16.2;2. A Gentle Majority Clause;185
16.3;3. Transparency, Calculability, and Abstract Generality;187
16.4;4. Success-Value Equality of the Deputies’ Votes;188
16.5;5. Preservation of the Majority by Means of D’Hondt;190
16.6;6. A Brutal Majority Clause;191
16.7;7. Preservation of the Majority by Means of Hill et al.;192
16.8;8. Minimum Seat Requirements;193
16.9;References;194
17;Allotment According to Preferential Vote: Ecuador’s Elections;196
17.1;1. Introduction;196
17.2;2. Unipersonal Election;197
17.2.1;2.1 The 2002 Presidential Election in Ecuador;197
17.2.2;2.2 Properties for Unipersonal Elections;198
17.3;3. The One-on-One Comparison Method;199
17.4;4. Choosing Several Representatives. Results for Different Elections;201
17.4.1;4.1 The Elections in the Spanish Universities;201
17.4.2;4.2 The Election of Ecuador’s Congress;203
17.5;5. Proportional Methods Based on Preferential Votes;205
17.6;6. Threshold of Representation for Different Methods;207
17.7;7. Some Remarks Regarding Borda-Type Proportional Methods;208
17.8;8. Other Proportional Methods Based on Preferential Vote;208
17.9;9. Ecuador’s Electoral System for Congress: a Brief Analysis;209
17.10;10. Conclusions;210
17.11;Acknowledgments;211
17.12;References;211
18;Degressively Proportional Methods for the Allotment of the European Parliament Seats Amongst the EU Member States;212
18.1;1. Introduction;212
18.2;2. Restrictions and Temporary Regulations in the Project of European Constitution;214
18.3;3. Several Quota Adjustments for Degressively Proportional Allotment in the EU;216
18.3.1;3.1 The Rectilinear Adjustment of Quotas;216
18.3.2;3.2 The Quota Adjustment with Parabolic Functions;217
18.3.3;3.3 The Quota Adjustment with Power-Type Functions;222
18.3.4;3.4 Other Quota Adjustment Functions;225
18.4;4. What Method to Use?;226
18.5;Acknowledgments;227
18.6;References;227
19;Hidden Mathematical Structures of Voting*;228
19.1;1. Introduction;228
19.2;2. Arrow’s Theorem;229
19.2.1;2.1 An Explanation;230
19.2.2;2.2 Finding Resolutions;231
19.3;3. McKelvey’s Chaos Theorem;232
19.4;4. Challenges;234
19.5;4.1 Plott Diagrams;235
19.6;5. Generic Existence of a Core;236
19.7;6. The Finesse Point;238
19.8;7. Selective Core and Finesse Point;240
19.9;8. Conclusion;240
19.10;References;241
20;A Comparison of Electoral Formulae for the Faroese Parliament;242
20.1;1. Introduction;242
20.2;2. Seat Bias of Apportionment Methods;244
20.3;3. District-Based Electoral Formulae;247
20.3.1;3.1 Vote Distributions;248
20.3.2;3.2 Performance Indices;248
20.3.3;3.3 Electoral Formulae;249
20.4;4. Results;251
20.5;5. Conclusion;252
20.6;References;257
21;List of Talks;259
21.1;Invited Talks;259
21.2;Contributed Talks;259
22;List of Participants;260
22.1;Invited Speakers;260
22.2;Further Participants;260
22.3;Scientific Co-Directors of the Workshop;260