Voting paradoxes and group coherence: the Condorcet efficiency of voting rules
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
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Berlin
Springer
2011
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| Series: | Studies in choice and welfare
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 385 S. 235 mm x 155 mm |
| ISBN: | 9783642031069 9783642031076 |
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| 100 | 1 | |a Gehrlein, William V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Voting paradoxes and group coherence |b the Condorcet efficiency of voting rules |c William V. Gehrlein ; Dominique Lepelley |
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IMAGE 1
CONTENTS
1 VOTING PARADOXES AND THEIR PROBABILITIES 1
1.1 INTRODUCTION 1
1.2 THE CASE OF MORE THAN TWO CANDIDATES 3
1.3 VOTING PARADOXES 5
1.3.1 INCOMPATIBILITY PARADOXES 5
1.3.2 MONOTONICITY PARADOXES 9
1.3.3 CHOICE SET VARIANCE PARADOXES 11
1.4 EMPIRICAL EVIDENCE OF THE EXISTENCE OF VOTING PARADOXES 12 1.4.1
EMPIRICAL EVIDENCE OF CONDORCET'S PARADOX 12
1.4.2 EMPIRICAL EVIDENCE OF BORDA'S PARADOX 15
1.5 PROBABILITY REPRESENTATIONS FOR VOTING PARADOXES 16
1.5.1 MULTINOMIAL PROBABILITY MODELS FOR VOTER PROFILES 17 1.5.2
MULTINOMIAL PROBABILITY MODELS - LIMITING CASE FOR H 21 1.5.3
PROBABILITY MODELS FOR VOTING SITUATIONS - ALGEBRAIC APPROACH 24
1.5.4 PROBABILITY MODELS FOR VOTING SITUATIONS - EUPIA 32 1.5.5
PROBABILITY MODELS - EHRHART POLYNOMIALS 35
1.5.6 PROBABILITY MODELS - BARVINOK'S ALGORITHM 38
1.6 RELEVANCE OF DC, IC, IAC AND MC BASED PROBABILITIES 40 1.6.1 GENERAL
ARGUMENTS 40
1.6.2 RESULTS FROM THE DC ASSUMPTION 42
1.6.3 RESULTS FROM IC-IAC COMPARISONS 43
1.6.4 HOMOGENEITY AND DEPENDENCE CONNECTIONS 45
1.7 CONCLUSION 47
2 CONDORCET'S PARADOX AND GROUP COHERENCE 49
2.1 INTRODUCTION 49
2.2 POPULATION SPECIFIC MEASURES OF HOMOGENEITY 49
2.3 SITUATION SPECIFIC MEASURES OF HOMOGENEITY 50
2.3.1 WEAK MEASURES OF GROUP COHERENCE 54
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000033953
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
2.3.2 STRONG MEASURES OF GROUP COHERENCE 56
2.4 OBTAINING PROBABILITY REPRESENTATIONS 57
2.4.1 EUPIA2 58
2.5 CUMULATIVE PROBABILITIES THAT A PMRW EXISTS 68
2.6 PROPORTIONS OF PROFILES WITH SPECIFIED PARAMETERS 71
2.7 RESULTS WITH STRONG MEASURES OF GROUP COHERENCE 73
2.8 CONCLUSION 78
3 OTHER INCOMPATIBILITY PARADOXES 81
3.1 INTRODUCTION 81
3.2 BORDA'S PARADOX 81
3.2.1 THE PROBABILITY OF OBSERVING A STRICT BORDA PARADOX 82 3.2.2 THE
PROBABILITY OF OBSERVING A STRONG BORDA PARADOX 94 3.2.3 OVERALL
PROBABILITIES FOR BORDA'S PARADOX 105
3.3 CONDORCET'S OTHER PARADOX 114
3.3.1 A MORE RELAXED CONDITION 117
3.3.2 ANOTHER CONDITION 118
3.4 CONCLUSION 120
4 OTHER VOTING PARADOXES 123
4.1 CHOICE SET VARIANCE PARADOXES 123
4.1.1 OSTROGORSKI'S PARADOX 123
4.1.2 THE MAJORITY PARADOX 141
4.2 MONOTONICITY PARADOXES 150
4.2.1 MONOTONICITY PARADOX PROBABILITIES 151
4.2.2 NO SHOW PARADOX PROBABILITIES 152
4.3 THE INSTABILITY PARADOX 153
4.4 CONCLUSION 1 54
5 CONDORCET EFFICIENCY AND SOCIAL HOMOGENEITY 157
5.1 INTRODUCTION 157
5.2 THE DESIRABILITY OF USING SIMPLE VOTING RULES 159
5.3 EARLY RESEARCH ON THE CONDORCET EFFICIENCY OF VOTING RULES 161 5.3.1
EARLY NUMERICAL ANALYSIS OF CONDORCET EFFICIENCY 161 5.3.2 PROBABILITY
REPRESENTATIONS FOR CONDORCET EFFICIENCY 169 5.3.3 SUMMARY OF CONDORCET
EFFICIENCY RESULTS 188
5.4 THE IMPACT OF SOCIAL HOMOGENEITY ON EFFICIENCY 190
5.4.1 POPULATION SPECIFIC MEASURES OF HOMOGENEITY 191 5.4.2 SITUATION
SPECIFIC MEASURES OF HOMOGENEITY 192
5.4.3 STRONG CONDORCET EFFICIENCY OF VOTING RULES 194
5.4.4 SPATIAL MODELING RESULTS 197
5.4.5 SUMMARY OF SOCIAL HOMOGENEITY RESULTS 198
IMAGE 3
CONTENTS XI
6 COHERENCE AND THE EFFICIENCY HYPOTHESIS 199
6.1 INTRODUCTION 199
6.2 NUMERICAL EVIDENCE 199
6.3 CONDORCET EFFICIENCY WITH SINGLE PEAKED PREFERENCES 201 6.4
EFFICIENCY WITH WEAK MEASURES OF GROUP COHERENCE 203 6.4.1 CONDORCET
EFFICIENCY OF PR WITH WEAK MEASURES 203 6.4.2 CONDORCET EFFICIENCY OF
NPR WITH WEAK MEASURES 209
6.4.3 CONDORCET EFFICIENCY OF BR WITH WEAK MEASURES 212 6.4.4
SINGLE-STAGE VOTING RULES WITH WEAK MEASURES 213 6.4.5 SINGLE-STAGE
VOTING RULES: A BORDA COMPROMISE 217 6.4.6 TWO-STAGE RULE EFFICIENCIES
WITH WEAK MEASURES 217 6.5 EFFICIENCY WITH STRONG MEASURES OF GROUP
COHERENCE 226
6.5.1 S INGLE-STAGE RULE REPRESENTATIONS WITH STRONG MEASURES - 229
6.5.2 SINGLE-STAGE RULE EFFICIENCIES WITH STRONG MEASURES 235 6.5.3
TWO-STAGE RULE REPRESENTATIONS WITH STRONG MEASURES 239 6.5.4 TWO-STAGE
RULE EFFICIENCIES WITH STRONG MEASURES 243 6.6 CONCLUSION 246
7 OTHER CHARACTERISTICS OF VOTING RULES 249
7.1 INTRODUCTION 249
7.2 EMPIRICAL STUDIES OF CONDORCET EFFICIENCY 249
7.2.1 SINGLE-STAGE VOTING RULES 249
7.2.2 TWO-STAGE VOTING RULES 252
7.3 PRACTICAL FACTORS AND CONDORCET EFFICIENCY 252
7.4 VOTER INDIFFERENCE AND CONDORCET EFFICIENCY 259
7.4.1 THE FORCED RANKING OPTION 259
7.4.2 MODIFYING WSR'S FOR VOTER INDIFFERENCE 266
7.5 VOTER ABSTENTION AND CONDORCET EFFICIENCY 269
7.5.1 TWO-CANDIDATE ELECTIONS 269
7.5.2 THREE-CANDIDATE ELECTIONS 270
7.6 THE PRESENCE OF A PMR CYCLE AND CONDORCET EFFICIENCY 276 7.6.1
METHODS FOR BREAKING PMR CYCLES 276
7.6.2 THE EFFICIENCY OF WSR'S WHEN PMR CYCLES EXIST 278 7.7 THE IMPACT
OF REMOVING CANDIDATES 282
7.8 RESULTS FROM SAARI'S ANALYSIS OF WSR'S 284
7.9 CHARACTERIZATIONS OF BR 287
7.10 POTENTIAL FOR MANIPULATION 289
7.10.1 EMPIRICAL RESULTS ON BR MANIPULABILITY 290
7.10.2 ANALYTICAL STUDIES OF BR MANIPULATION 290
7.11 CONCLUSION 294
8 THE SIGNIFICANCE OF VOTING RULE SELECTION 295
8.1 INTRODUCTION 295
8.2 SAME WINNER WITH TWO VOTING RULES 295
IMAGE 4
XUE CONTENTS
8.2.1 TWO VOTING RULES WINNER COINCIDENCE 295
8.2.2 TWO VOTING RULES WINNER COINCIDENCE WITH THE PMRW . 296 8.3 THE
PROBABILITY THAT ALL WSR'S ELECT THE SAME WINNER 299 8.4 HOMOGENEITY AND
VOTING RULE SELECTION SENSITIVITY 302 8.5 MEASURES OF COHERENCE AND
VOTING RULE SELECTION SENSITIVITY 303
8.5.1 WEAK MEASURES AND WSR SELECTION SENSITIVITY 307 8.5.2 STRONG
MEASURES AND WSR SELECTION SENSITIVITY 310 8.6 OTHER VOTING RULES 314
8.6.1 APPROVAL VOTING 314
8.6.2 LOTTERY BASED VOTING RULES 322
8.6.3 MEDIAN VOTING RULE 326
8.7 CONCLUSION 328
9 COMPLETE PMR RANKING EFFICIENCIES 331
9.1 INTRODUCTION 331
9.2 CANDIDATE RANKING SENSITIVITY TO WSR SELECTION 331
9.2.1 EMPIRICAL RESULTS 332
9.2.2 PROBABILITY REPRESENTATIONS FOR THE SAME WSR RANKING 333 9.3
CONDORCET RANKING EFFICIENCY 333
9.3.1 EMPIRICAL RESULTS 335
9.3.2 THE IMPACT OF SOCIAL HOMOGENEITY 335
9.3.3 THE PRESENCE OF A PMR CYCLE 337
9.3.4 THE IMPACT OF GROUP MUTUAL COHERENCE 339
9.4 CONDORCET COMMITTEES 357
9.4.1 COMMITTEE ELECTION PARADOXES 357
9.4.2 CONDORCET COMMITTEE DEFINITIONS 359
9.4.3 CONDORCET COMMITTEE EFFICIENCY 364
9.4.4 CONDORCET COMMITTEE EFFICIENCY SUMMARY 366
REFERENCES 367
INDEX 381 |
| any_adam_object | 1 |
| author | Gehrlein, William V. Lepelley, Dominique |
| author_facet | Gehrlein, William V. Lepelley, Dominique |
| author_role | aut aut |
| author_sort | Gehrlein, William V. |
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| dewey-full | 324 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 324 - The political process |
| dewey-raw | 324 |
| dewey-search | 324 |
| dewey-sort | 3324 |
| dewey-tens | 320 - Political science (Politics and government) |
| discipline | Politologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2024-07-20T10:45:24Z |
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| isbn | 9783642031069 9783642031076 |
| language | English |
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| physical | XII, 385 S. 235 mm x 155 mm |
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| spelling | Gehrlein, William V. Verfasser aut Voting paradoxes and group coherence the Condorcet efficiency of voting rules William V. Gehrlein ; Dominique Lepelley Berlin Springer 2011 XII, 385 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Studies in choice and welfare Mathematisches Problem (DE-588)4114530-6 gnd rswk-swf Wahlverhalten (DE-588)4079009-5 gnd rswk-swf Wahlverhalten (DE-588)4079009-5 s Mathematisches Problem (DE-588)4114530-6 s DE-604 Lepelley, Dominique Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423798&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020568593&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gehrlein, William V. Lepelley, Dominique Voting paradoxes and group coherence the Condorcet efficiency of voting rules Mathematisches Problem (DE-588)4114530-6 gnd Wahlverhalten (DE-588)4079009-5 gnd |
| subject_GND | (DE-588)4114530-6 (DE-588)4079009-5 |
| title | Voting paradoxes and group coherence the Condorcet efficiency of voting rules |
| title_auth | Voting paradoxes and group coherence the Condorcet efficiency of voting rules |
| title_exact_search | Voting paradoxes and group coherence the Condorcet efficiency of voting rules |
| title_full | Voting paradoxes and group coherence the Condorcet efficiency of voting rules William V. Gehrlein ; Dominique Lepelley |
| title_fullStr | Voting paradoxes and group coherence the Condorcet efficiency of voting rules William V. Gehrlein ; Dominique Lepelley |
| title_full_unstemmed | Voting paradoxes and group coherence the Condorcet efficiency of voting rules William V. Gehrlein ; Dominique Lepelley |
| title_short | Voting paradoxes and group coherence |
| title_sort | voting paradoxes and group coherence the condorcet efficiency of voting rules |
| title_sub | the Condorcet efficiency of voting rules |
| topic | Mathematisches Problem (DE-588)4114530-6 gnd Wahlverhalten (DE-588)4079009-5 gnd |
| topic_facet | Mathematisches Problem Wahlverhalten |
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