Cycles and social choice :: the true and unabridged story of a most protean paradox /
This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2018.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781316853238 1316853233 9781107180918 1107180910 9781316848371 131684837X 1316632377 9781316632376 |
Internformat
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| 245 | 1 | 0 | |a Cycles and social choice : |b the true and unabridged story of a most protean paradox / |c Thomas Schwartz, University of California, Los Angeles. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2018. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed March 5, 2018). | |
| 505 | 0 | |a Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Acknowledgements; Introduction; 1 Condorcet's Two Discoveries; 1.1 The Rejection of Condorcet Winners; 1.2 The Paradox of Voting; 1.3 What the Paradox Means and Does Not; 1.4 Why Majorities: May's Theorem; 1.5 More than Cycles: McGarvey's Theorem; 1.6 Beyond Majority Rule: Ward's Theorem; 1.7 Individual Rights: Sen's Paradox; 1.8 A Word about Words; 2 Incidence of the Paradox; 2.1 Black's Median-Stability Theorem; 2.2 Generalizations of Single Peakedness | |
| 505 | 8 | |a 2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem | |
| 505 | 8 | |a 4 Arrovian Cycle Theorems4.1 First Relaxation: Transitive Social Preference; 4.2 From »-Transitivity to Acyclicity, Assuming n Alternatives; 4.3 Wrong Turn: Positive Responsiveness; 4.4 Three or More Alternatives and a Reasonable Limit on Ties: (2k -- 2)-Resoluteness; 4.5 A Side Trip to Interpersonally Comparable Cardinal Utilities; 4.6 Proof of Inconsistency; 5 Second Line of Cycle Theorems: Condorcet Generalizations; 5.1 Simple Latin-Square Constructions: The Theorems of Ward, Brown, and Nakamura; 5.2 A General Condition for Cycles; 5.3 Proof that Cycles are Allowed | |
| 505 | 8 | |a 5.4 How Earlier Results and Proofs Fit the Pattern5.5 Individual Indifference and the Most General Cycle-Sufficiency Condition of All; 5.6 The Necessity Theorem; 6 Top Cycles in a Fixed Feasible Set; 6.1 New Bottle, Old Wines; 6.2 Top Cycles; 6.3 Tricycles and All-Inclusive Tight Cycles; 6.4 Absorbing Old Assumptions; 7 Strategic Consequences of Cycles; 7.1 Vote Manipulation; 7.2 Proof that Cycles Ensure Manipulability, and a Slight Generalization; 7.3 Comparison with Other Theorems; 7.4 Consequences of Nonmanipulability proved: The Duggan-Schwartz Theorem; 7.5 Cycles and Game Solutions | |
| 505 | 8 | |a 7.6 Proof that Cycles Block Nash Implementation8 Structural Consequences of Cycles; 8.1 Agenda Control: Trees; 8.2 Dendriform Details; 8.3 Agenda Control: Sets; 8.4 Agenda Control: Joining and Dividing Questions; 8.5 Cycles and Paradoxical Power; 8.6 Cycles, External Costs, and Political Parties; 9 Questions about Prediction and Explanation; 9.1 What Majorities Would Choose; 9.2 Proof that (1)-(4) Characterize TEQ; 9.3 Examples and Comparisons of TEQ with Other Solutions; 9.4 A Different Approach to Cooperative Solutions; 9.5 Beyond Tournaments; 9.6 Methodological Asides: The Use of Axioms | |
| 520 | |a This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice. | ||
| 650 | 0 | |a Voting |x Mathematical models. | |
| 650 | 0 | |a Social choice. |0 http://id.loc.gov/authorities/subjects/sh85123920 | |
| 650 | 6 | |a Vote |x Modèles mathématiques. | |
| 650 | 6 | |a Choix collectif. | |
| 650 | 7 | |a POLITICAL SCIENCE |x Government |x General. |2 bisacsh | |
| 650 | 7 | |a POLITICAL SCIENCE |x Political Process |x Elections. |2 bisacsh | |
| 650 | 7 | |a POLITICAL SCIENCE |x Political Process |x General. |2 bisacsh | |
| 650 | 7 | |a Social choice |2 fast | |
| 650 | 7 | |a Voting |x Mathematical models |2 fast | |
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| 776 | 0 | 8 | |i Print version: |a Schwartz, Thomas, 1943- |t Cycles and social choice. |d Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018 |z 1107180910 |z 9781107180918 |w (DLC) 2017052586 |w (OCoLC)1011557275 |
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| author | Schwartz, Thomas, 1943- |
| author_GND | http://id.loc.gov/authorities/names/n2017067162 |
| author_facet | Schwartz, Thomas, 1943- |
| author_role | aut |
| author_sort | Schwartz, Thomas, 1943- |
| author_variant | t s ts |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | J - Political Science |
| callnumber-label | JF1001 |
| callnumber-raw | JF1001 .S38 2017 |
| callnumber-search | JF1001 .S38 2017 |
| callnumber-sort | JF 41001 S38 42017 |
| callnumber-subject | JF - Public Administration |
| collection | ZDB-4-EBA |
| contents | Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Acknowledgements; Introduction; 1 Condorcet's Two Discoveries; 1.1 The Rejection of Condorcet Winners; 1.2 The Paradox of Voting; 1.3 What the Paradox Means and Does Not; 1.4 Why Majorities: May's Theorem; 1.5 More than Cycles: McGarvey's Theorem; 1.6 Beyond Majority Rule: Ward's Theorem; 1.7 Individual Rights: Sen's Paradox; 1.8 A Word about Words; 2 Incidence of the Paradox; 2.1 Black's Median-Stability Theorem; 2.2 Generalizations of Single Peakedness 2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem 4 Arrovian Cycle Theorems4.1 First Relaxation: Transitive Social Preference; 4.2 From »-Transitivity to Acyclicity, Assuming n Alternatives; 4.3 Wrong Turn: Positive Responsiveness; 4.4 Three or More Alternatives and a Reasonable Limit on Ties: (2k -- 2)-Resoluteness; 4.5 A Side Trip to Interpersonally Comparable Cardinal Utilities; 4.6 Proof of Inconsistency; 5 Second Line of Cycle Theorems: Condorcet Generalizations; 5.1 Simple Latin-Square Constructions: The Theorems of Ward, Brown, and Nakamura; 5.2 A General Condition for Cycles; 5.3 Proof that Cycles are Allowed 5.4 How Earlier Results and Proofs Fit the Pattern5.5 Individual Indifference and the Most General Cycle-Sufficiency Condition of All; 5.6 The Necessity Theorem; 6 Top Cycles in a Fixed Feasible Set; 6.1 New Bottle, Old Wines; 6.2 Top Cycles; 6.3 Tricycles and All-Inclusive Tight Cycles; 6.4 Absorbing Old Assumptions; 7 Strategic Consequences of Cycles; 7.1 Vote Manipulation; 7.2 Proof that Cycles Ensure Manipulability, and a Slight Generalization; 7.3 Comparison with Other Theorems; 7.4 Consequences of Nonmanipulability proved: The Duggan-Schwartz Theorem; 7.5 Cycles and Game Solutions 7.6 Proof that Cycles Block Nash Implementation8 Structural Consequences of Cycles; 8.1 Agenda Control: Trees; 8.2 Dendriform Details; 8.3 Agenda Control: Sets; 8.4 Agenda Control: Joining and Dividing Questions; 8.5 Cycles and Paradoxical Power; 8.6 Cycles, External Costs, and Political Parties; 9 Questions about Prediction and Explanation; 9.1 What Majorities Would Choose; 9.2 Proof that (1)-(4) Characterize TEQ; 9.3 Examples and Comparisons of TEQ with Other Solutions; 9.4 A Different Approach to Cooperative Solutions; 9.5 Beyond Tournaments; 9.6 Methodological Asides: The Use of Axioms |
| ctrlnum | (OCoLC)1027218413 |
| dewey-full | 324.601 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 324 - The political process |
| dewey-raw | 324.601 |
| dewey-search | 324.601 |
| dewey-sort | 3324.601 |
| dewey-tens | 320 - Political science (Politics and government) |
| discipline | Politologie |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:28:14Z |
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| spelling | Schwartz, Thomas, 1943- author. https://id.oclc.org/worldcat/entity/E39PCjwYVVpf8rwxRv8gqGfpKb http://id.loc.gov/authorities/names/n2017067162 Cycles and social choice : the true and unabridged story of a most protean paradox / Thomas Schwartz, University of California, Los Angeles. Cambridge : Cambridge University Press, 2018. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Online resource; title from PDF title page (EBSCO, viewed March 5, 2018). Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Acknowledgements; Introduction; 1 Condorcet's Two Discoveries; 1.1 The Rejection of Condorcet Winners; 1.2 The Paradox of Voting; 1.3 What the Paradox Means and Does Not; 1.4 Why Majorities: May's Theorem; 1.5 More than Cycles: McGarvey's Theorem; 1.6 Beyond Majority Rule: Ward's Theorem; 1.7 Individual Rights: Sen's Paradox; 1.8 A Word about Words; 2 Incidence of the Paradox; 2.1 Black's Median-Stability Theorem; 2.2 Generalizations of Single Peakedness 2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem 4 Arrovian Cycle Theorems4.1 First Relaxation: Transitive Social Preference; 4.2 From »-Transitivity to Acyclicity, Assuming n Alternatives; 4.3 Wrong Turn: Positive Responsiveness; 4.4 Three or More Alternatives and a Reasonable Limit on Ties: (2k -- 2)-Resoluteness; 4.5 A Side Trip to Interpersonally Comparable Cardinal Utilities; 4.6 Proof of Inconsistency; 5 Second Line of Cycle Theorems: Condorcet Generalizations; 5.1 Simple Latin-Square Constructions: The Theorems of Ward, Brown, and Nakamura; 5.2 A General Condition for Cycles; 5.3 Proof that Cycles are Allowed 5.4 How Earlier Results and Proofs Fit the Pattern5.5 Individual Indifference and the Most General Cycle-Sufficiency Condition of All; 5.6 The Necessity Theorem; 6 Top Cycles in a Fixed Feasible Set; 6.1 New Bottle, Old Wines; 6.2 Top Cycles; 6.3 Tricycles and All-Inclusive Tight Cycles; 6.4 Absorbing Old Assumptions; 7 Strategic Consequences of Cycles; 7.1 Vote Manipulation; 7.2 Proof that Cycles Ensure Manipulability, and a Slight Generalization; 7.3 Comparison with Other Theorems; 7.4 Consequences of Nonmanipulability proved: The Duggan-Schwartz Theorem; 7.5 Cycles and Game Solutions 7.6 Proof that Cycles Block Nash Implementation8 Structural Consequences of Cycles; 8.1 Agenda Control: Trees; 8.2 Dendriform Details; 8.3 Agenda Control: Sets; 8.4 Agenda Control: Joining and Dividing Questions; 8.5 Cycles and Paradoxical Power; 8.6 Cycles, External Costs, and Political Parties; 9 Questions about Prediction and Explanation; 9.1 What Majorities Would Choose; 9.2 Proof that (1)-(4) Characterize TEQ; 9.3 Examples and Comparisons of TEQ with Other Solutions; 9.4 A Different Approach to Cooperative Solutions; 9.5 Beyond Tournaments; 9.6 Methodological Asides: The Use of Axioms This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice. Voting Mathematical models. Social choice. http://id.loc.gov/authorities/subjects/sh85123920 Vote Modèles mathématiques. Choix collectif. POLITICAL SCIENCE Government General. bisacsh POLITICAL SCIENCE Political Process Elections. bisacsh POLITICAL SCIENCE Political Process General. bisacsh Social choice fast Voting Mathematical models fast has work: Cycles and social choice (Text) https://id.oclc.org/worldcat/entity/E39PCGbcwKjJYqQ9PWhfdkQhjK https://id.oclc.org/worldcat/ontology/hasWork Print version: Schwartz, Thomas, 1943- Cycles and social choice. Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018 1107180910 9781107180918 (DLC) 2017052586 (OCoLC)1011557275 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1694403 Volltext |
| spellingShingle | Schwartz, Thomas, 1943- Cycles and social choice : the true and unabridged story of a most protean paradox / Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Acknowledgements; Introduction; 1 Condorcet's Two Discoveries; 1.1 The Rejection of Condorcet Winners; 1.2 The Paradox of Voting; 1.3 What the Paradox Means and Does Not; 1.4 Why Majorities: May's Theorem; 1.5 More than Cycles: McGarvey's Theorem; 1.6 Beyond Majority Rule: Ward's Theorem; 1.7 Individual Rights: Sen's Paradox; 1.8 A Word about Words; 2 Incidence of the Paradox; 2.1 Black's Median-Stability Theorem; 2.2 Generalizations of Single Peakedness 2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem 4 Arrovian Cycle Theorems4.1 First Relaxation: Transitive Social Preference; 4.2 From »-Transitivity to Acyclicity, Assuming n Alternatives; 4.3 Wrong Turn: Positive Responsiveness; 4.4 Three or More Alternatives and a Reasonable Limit on Ties: (2k -- 2)-Resoluteness; 4.5 A Side Trip to Interpersonally Comparable Cardinal Utilities; 4.6 Proof of Inconsistency; 5 Second Line of Cycle Theorems: Condorcet Generalizations; 5.1 Simple Latin-Square Constructions: The Theorems of Ward, Brown, and Nakamura; 5.2 A General Condition for Cycles; 5.3 Proof that Cycles are Allowed 5.4 How Earlier Results and Proofs Fit the Pattern5.5 Individual Indifference and the Most General Cycle-Sufficiency Condition of All; 5.6 The Necessity Theorem; 6 Top Cycles in a Fixed Feasible Set; 6.1 New Bottle, Old Wines; 6.2 Top Cycles; 6.3 Tricycles and All-Inclusive Tight Cycles; 6.4 Absorbing Old Assumptions; 7 Strategic Consequences of Cycles; 7.1 Vote Manipulation; 7.2 Proof that Cycles Ensure Manipulability, and a Slight Generalization; 7.3 Comparison with Other Theorems; 7.4 Consequences of Nonmanipulability proved: The Duggan-Schwartz Theorem; 7.5 Cycles and Game Solutions 7.6 Proof that Cycles Block Nash Implementation8 Structural Consequences of Cycles; 8.1 Agenda Control: Trees; 8.2 Dendriform Details; 8.3 Agenda Control: Sets; 8.4 Agenda Control: Joining and Dividing Questions; 8.5 Cycles and Paradoxical Power; 8.6 Cycles, External Costs, and Political Parties; 9 Questions about Prediction and Explanation; 9.1 What Majorities Would Choose; 9.2 Proof that (1)-(4) Characterize TEQ; 9.3 Examples and Comparisons of TEQ with Other Solutions; 9.4 A Different Approach to Cooperative Solutions; 9.5 Beyond Tournaments; 9.6 Methodological Asides: The Use of Axioms Voting Mathematical models. Social choice. http://id.loc.gov/authorities/subjects/sh85123920 Vote Modèles mathématiques. Choix collectif. POLITICAL SCIENCE Government General. bisacsh POLITICAL SCIENCE Political Process Elections. bisacsh POLITICAL SCIENCE Political Process General. bisacsh Social choice fast Voting Mathematical models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85123920 |
| title | Cycles and social choice : the true and unabridged story of a most protean paradox / |
| title_auth | Cycles and social choice : the true and unabridged story of a most protean paradox / |
| title_exact_search | Cycles and social choice : the true and unabridged story of a most protean paradox / |
| title_full | Cycles and social choice : the true and unabridged story of a most protean paradox / Thomas Schwartz, University of California, Los Angeles. |
| title_fullStr | Cycles and social choice : the true and unabridged story of a most protean paradox / Thomas Schwartz, University of California, Los Angeles. |
| title_full_unstemmed | Cycles and social choice : the true and unabridged story of a most protean paradox / Thomas Schwartz, University of California, Los Angeles. |
| title_short | Cycles and social choice : |
| title_sort | cycles and social choice the true and unabridged story of a most protean paradox |
| title_sub | the true and unabridged story of a most protean paradox / |
| topic | Voting Mathematical models. Social choice. http://id.loc.gov/authorities/subjects/sh85123920 Vote Modèles mathématiques. Choix collectif. POLITICAL SCIENCE Government General. bisacsh POLITICAL SCIENCE Political Process Elections. bisacsh POLITICAL SCIENCE Political Process General. bisacsh Social choice fast Voting Mathematical models fast |
| topic_facet | Voting Mathematical models. Social choice. Vote Modèles mathématiques. Choix collectif. POLITICAL SCIENCE Government General. POLITICAL SCIENCE Political Process Elections. POLITICAL SCIENCE Political Process General. Social choice Voting Mathematical models |
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