Disposing dictators, demystifying voting paradoxes: social choice analysis
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 240 S. Ill., graph. Darst. |
| ISBN: | 9780521516051 9780521731607 |
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| 245 | 1 | 0 | |a Disposing dictators, demystifying voting paradoxes |b social choice analysis |c Donald G. Saari |
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Record in the Search Index
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| adam_text | CONTENTS PREFACE PAGEXI 1 SUBTLE COMPLEXITY OF SOCIAL CHOICE 1 1.1 DOES
EVERYTHING GO WRONG? 1 1.2 AND THE PROUD FATHER IS... 3 1.3 ENEMIES? 7
1.4 CURSE OF DIMENSIONALITY 13 1.5 OUTLINE 15 1.5.1 DETHRONING
DICTATORS, AND THEN PARADOXES 16 1.5.2 THE WILL OF THE VOTERS : WHAT IS
IT? 18 2 DETHRONING DICTATORS 20 2.1 MAJOR NEGATIVE CONCLUSIONS 21 2.1.1
ARROW S THEOREM 21 2.1.2 S EN S SEMINAL RESULT 23 2.1.3 TOPOLOGICAL
DICTATORS 26 2.1.4 PARADOX OF VOTING AND CONDORCET S TRIPLETS 28 2.1.5
LIST S LISTS 29 2.1.6 ANSCOMBE 30 2.1.7 A STANDARD REQUIREMENT 31 2.2
COMMONALITY 31 2.2.1 CONDORCET S IDEAS DOMINATE 32 2.2.2 CAN WE TRUST
THE MAJORITY VOTING OVER PAIRS? 40 2.2.3 A COMMON EXPLANATION 42 VII V M
CONTENTS 2.3 WHY DO THESE NEGATIVE RESULTS OCCUR? 43 2.3.1 ARROW S
THEOREM 44 2.3.2 SEN S RESULT 47 2.3.3 TOPOLOGICAL DICTATORS AND BEACH
PARTIES 51 2.4 POSITIVE REPLACEMENTS 58 2.4.1 ARROW S RESULT 58 2.4.2
SEN S RESULT 64 2.4.3 TOPOLOGICAL DICTATORS AND MORE EFFECTIVE AGENTS 70
2.5 FINAL THOUGHTS 72 3 VOTING DICTIONARIES 74 3.1 WHAT GOES WRONG? 76
3.1.1 AXIOMATIC APPROACH VERSUS PARADOXES 77 3.1.2 DICTIONARIES 77 3.1.3
AGGREGATION RULES 80 3.2 LASSIE AND THE AXIOMATIC APPROACH 81 3.3
DICTIONARIES 84 3.3.1 A LITTLE CHAOS 86 3.3.2 CHAOS WITHIN VOTING THEORY
90 3.3.3 DICTIONARY LISTINGS FOR POSITIONAL RULES 91 3.4 USING THE
DICTIONARIES 96 3.4.1 VARIETY COMING FROM VARIETIES 99 3.4.2 OTHER
DICTIONARIES 104 3.5 COMPARING OUTCOMES OVER A SET OF CANDIDATES 107
3.5.1 GENERAL RESULTS 107 3.5.2 LET ELEMENTARY GEOMETRY DO THE WORK 109
3.5.3 PROCEDURE LINES 111 3.5.4 OTHER RULES, SUCH AS APPROVAL VOTING 113
3.5.5 A WORKING TOOL FOR ACTUAL ELECTIONS * 116 3.5.6 BACK TO THE
ORIGINAL PROBLEM: CREATING EXAMPLES 118 4 EXPLAINING ALL VOTING
PARADOXES 123 4.1 PROFILE COORDINATES 124 4.1.1 COFFEE REFLECTIONS 124
4.1.2 THE WATER FOR VOTING RULES 127 4.1.3 NOTHING GOES WRONG 133
CONTENTS IX 4.1.4 A CREAMY ADDITION: POSITIONAL DIFFERENCES 139 4.1.5
ANYTHING CAN HAPPEN 144 4.1.6 SUGAR AND SPICE, AND ALL THOSE NICE CYCLES
146 4.1.7 DIFFERENCES BETWEEN BORDA AND CONDORCET 157 4.1.8 KEMENY,
DODGSON, AND OTHER SYSTEMS; WHO CARES? 158 4.2 ALL POSSIBLE
THREE-CANDIDATE OUTCOMES 160 4.2.1 CREATING EXAMPLES 161 4.2.2
CONVERTING MOLECULES INTO COFFEE, SUGAR, AND CREAM COORDINATES 162 4.3
THE WILL OF THE VOTERS 165 4.3.1 SELECTING CONDITIONS 166 4.3.2
IDENTIFYING THE VOTERS WISHES 168 4.3.3 EXTENSIONS AND QUESTIONS 170 4.4
TEASER ABOUT MORE CANDIDATES 170 4.4.1 DESIGNING PROFILE CONFIGURATIONS
171 4.4.2 AN INTERESTING RELATIONSHIP 172 4.4.3 A NEW APPROACH 175 4.5
FINDING AND PROVING NEW THEOREMS 178 4.5.1 SPECIAL CASE; THREE
CANDIDATES 180 4.5.2 CONDORCET WINNERS AND LOSERS 180 4.5.3 BORDA
WINNERS AND LOSERS 181 4.5.4 LOW-HANGING FRUIT WITH N CANDIDATES 182
4.5.5 BORDA VERSUS PAIRWISE RANKINGS 183 4.5.6 BORDA VERSUS BORDA
RANKINGS 187 DELIVER US FROM THE PLURALITY VOTE 190 5.1 OUR STANDARD
VOTING RULE 190 5.1.1 THE 2000 U.S. PRESIDENTIAL ELECTION 191 5.1.2 THE
2002 FRENCH PRESIDENTIAL ELECTION 192 5.1.3 REFORM, OR FIGHTING TERMITES
WITH PAINT AND PUTTY? 195 5.1.4 RESOLUTIONS, BUT OTHER PROBLEMS 197 5.2
NEWTON S THIRD LAW OF POLITICS 198 5.2.1 COMPARISON WITH PAIRWISE VOTING
200 5.2.2 STABILITY AND THE CORE 202 5.2.3 MCKELVEY S CHAOS THEOREM 206
5.3 GENERIC STABILITY OF THE CORE 208 X CONTENTS 5.4 MORE ABOUT CYCLES
AND CHAOS 211 5.4.1 CONDORCET N-CYCLES 212 5.4.2 CONTROLLING CHAOS 213
5.5 FINAL COMMENTS 214 6 APPENDIX EXTENDING THE UPSET CHILD EXAMPLE 218
6.1 SOURCE OF THE PROBLEM 219 6.2 GENERALIZATIONS 222 6.3 LEVEL SETS 226
REFERENCES 231 INDEX 23 7
|
| adam_txt |
CONTENTS PREFACE PAGEXI 1 SUBTLE COMPLEXITY OF SOCIAL CHOICE 1 1.1 DOES
EVERYTHING GO WRONG? 1 1.2 AND THE PROUD FATHER IS. 3 1.3 ENEMIES? 7
1.4 CURSE OF DIMENSIONALITY 13 1.5 OUTLINE 15 1.5.1 DETHRONING
DICTATORS, AND THEN PARADOXES 16 1.5.2 THE "WILL OF THE VOTERS": WHAT IS
IT? 18 2 DETHRONING DICTATORS 20 2.1 MAJOR NEGATIVE CONCLUSIONS 21 2.1.1
ARROW'S THEOREM 21 2.1.2 S EN'S SEMINAL RESULT 23 2.1.3 TOPOLOGICAL
DICTATORS 26 2.1.4 "PARADOX OF VOTING" AND CONDORCET'S TRIPLETS 28 2.1.5
LIST'S LISTS 29 2.1.6 ANSCOMBE 30 2.1.7 A STANDARD REQUIREMENT 31 2.2
COMMONALITY 31 2.2.1 CONDORCET'S IDEAS DOMINATE 32 2.2.2 CAN WE TRUST
THE MAJORITY VOTING OVER PAIRS? 40 2.2.3 A COMMON EXPLANATION 42 VII V'M
CONTENTS 2.3 WHY DO THESE NEGATIVE RESULTS OCCUR? 43 2.3.1 ARROW'S
THEOREM 44 2.3.2 SEN'S RESULT 47 2.3.3 TOPOLOGICAL DICTATORS AND BEACH
PARTIES 51 2.4 POSITIVE REPLACEMENTS 58 2.4.1 ARROW'S RESULT 58 2.4.2
SEN'S RESULT 64 2.4.3 TOPOLOGICAL DICTATORS AND MORE EFFECTIVE AGENTS 70
2.5 FINAL THOUGHTS 72 3 VOTING DICTIONARIES 74 3.1 WHAT GOES WRONG? 76
3.1.1 AXIOMATIC APPROACH VERSUS PARADOXES 77 3.1.2 DICTIONARIES 77 3.1.3
AGGREGATION RULES 80 3.2 LASSIE AND THE AXIOMATIC APPROACH 81 3.3
DICTIONARIES 84 3.3.1 A LITTLE CHAOS 86 3.3.2 CHAOS WITHIN VOTING THEORY
90 3.3.3 DICTIONARY LISTINGS FOR POSITIONAL RULES 91 3.4 USING THE
DICTIONARIES 96 3.4.1 VARIETY COMING FROM VARIETIES 99 3.4.2 OTHER
DICTIONARIES 104 3.5 COMPARING OUTCOMES OVER A SET OF CANDIDATES 107
3.5.1 GENERAL RESULTS 107 3.5.2 LET ELEMENTARY GEOMETRY DO THE WORK 109
3.5.3 PROCEDURE LINES 111 3.5.4 OTHER RULES, SUCH AS APPROVAL VOTING 113
3.5.5 A WORKING TOOL FOR ACTUAL ELECTIONS * 116 3.5.6 BACK TO THE
ORIGINAL PROBLEM: CREATING EXAMPLES 118 4 EXPLAINING ALL VOTING
PARADOXES 123 4.1 PROFILE COORDINATES 124 4.1.1 COFFEE REFLECTIONS 124
4.1.2 THE "WATER" FOR VOTING RULES 127 4.1.3 NOTHING GOES WRONG 133
CONTENTS IX 4.1.4 A CREAMY ADDITION: POSITIONAL DIFFERENCES 139 4.1.5
ANYTHING CAN HAPPEN 144 4.1.6 SUGAR AND SPICE, AND ALL THOSE NICE CYCLES
146 4.1.7 DIFFERENCES BETWEEN BORDA AND CONDORCET 157 4.1.8 KEMENY,
DODGSON, AND OTHER SYSTEMS; WHO CARES? 158 4.2 ALL POSSIBLE
THREE-CANDIDATE OUTCOMES 160 4.2.1 CREATING EXAMPLES 161 4.2.2
CONVERTING MOLECULES INTO COFFEE, SUGAR, AND CREAM COORDINATES 162 4.3
THE WILL OF THE VOTERS 165 4.3.1 SELECTING CONDITIONS 166 4.3.2
IDENTIFYING THE VOTERS'WISHES 168 4.3.3 EXTENSIONS AND QUESTIONS 170 4.4
TEASER ABOUT MORE CANDIDATES 170 4.4.1 DESIGNING PROFILE CONFIGURATIONS
171 4.4.2 AN INTERESTING RELATIONSHIP 172 4.4.3 A NEW APPROACH 175 4.5
FINDING AND PROVING NEW THEOREMS 178 4.5.1 SPECIAL CASE; THREE
CANDIDATES 180 4.5.2 CONDORCET WINNERS AND LOSERS 180 4.5.3 BORDA
WINNERS AND LOSERS 181 4.5.4 LOW-HANGING FRUIT WITH N CANDIDATES 182
4.5.5 BORDA VERSUS PAIRWISE RANKINGS 183 4.5.6 BORDA VERSUS BORDA
RANKINGS 187 DELIVER US FROM THE PLURALITY VOTE 190 5.1 OUR STANDARD
VOTING RULE 190 5.1.1 THE 2000 U.S. PRESIDENTIAL ELECTION 191 5.1.2 THE
2002 FRENCH PRESIDENTIAL ELECTION 192 5.1.3 REFORM, OR FIGHTING TERMITES
WITH PAINT AND PUTTY? 195 5.1.4 RESOLUTIONS, BUT OTHER PROBLEMS 197 5.2
NEWTON'S THIRD LAW OF POLITICS 198 5.2.1 COMPARISON WITH PAIRWISE VOTING
200 5.2.2 STABILITY AND THE CORE 202 5.2.3 MCKELVEY'S CHAOS THEOREM 206
5.3 GENERIC STABILITY OF THE CORE 208 X CONTENTS 5.4 MORE ABOUT CYCLES
AND CHAOS 211 5.4.1 CONDORCET N-CYCLES 212 5.4.2 CONTROLLING CHAOS 213
5.5 FINAL COMMENTS 214 6 APPENDIX EXTENDING THE UPSET CHILD EXAMPLE 218
6.1 SOURCE OF THE PROBLEM 219 6.2 GENERALIZATIONS 222 6.3 LEVEL SETS 226
REFERENCES 231 INDEX 23 7 |
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| id | DE-604.BV035066708 |
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| index_date | 2024-07-02T22:02:34Z |
| indexdate | 2024-07-09T21:21:26Z |
| institution | BVB |
| isbn | 9780521516051 9780521731607 |
| language | English |
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| physical | XV, 240 S. Ill., graph. Darst. |
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| spelling | Saari, Donald 1940- Verfasser (DE-588)124637418 aut Disposing dictators, demystifying voting paradoxes social choice analysis Donald G. Saari 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XV, 240 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Social choice Voting Elections Wahlverhalten (DE-588)4079009-5 gnd rswk-swf Kollektiventscheidung (DE-588)4022393-0 gnd rswk-swf Wahlverhalten (DE-588)4079009-5 s Kollektiventscheidung (DE-588)4022393-0 s DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016735149&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saari, Donald 1940- Disposing dictators, demystifying voting paradoxes social choice analysis Social choice Voting Elections Wahlverhalten (DE-588)4079009-5 gnd Kollektiventscheidung (DE-588)4022393-0 gnd |
| subject_GND | (DE-588)4079009-5 (DE-588)4022393-0 |
| title | Disposing dictators, demystifying voting paradoxes social choice analysis |
| title_auth | Disposing dictators, demystifying voting paradoxes social choice analysis |
| title_exact_search | Disposing dictators, demystifying voting paradoxes social choice analysis |
| title_exact_search_txtP | Disposing dictators, demystifying voting paradoxes social choice analysis |
| title_full | Disposing dictators, demystifying voting paradoxes social choice analysis Donald G. Saari |
| title_fullStr | Disposing dictators, demystifying voting paradoxes social choice analysis Donald G. Saari |
| title_full_unstemmed | Disposing dictators, demystifying voting paradoxes social choice analysis Donald G. Saari |
| title_short | Disposing dictators, demystifying voting paradoxes |
| title_sort | disposing dictators demystifying voting paradoxes social choice analysis |
| title_sub | social choice analysis |
| topic | Social choice Voting Elections Wahlverhalten (DE-588)4079009-5 gnd Kollektiventscheidung (DE-588)4022393-0 gnd |
| topic_facet | Social choice Voting Elections Wahlverhalten Kollektiventscheidung |
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