Mathematics of Decisions, Elections, and Games.

Intro -- Preface -- Redistricting and district compactness -- 1. Introduction: Redistricting and Gerrymandering -- 2. Measuring Compactness -- 3. Criteria for Compactness Measures and Discussion -- References -- Fair division and redistricting -- 1. Introduction -- 2. Fair Division -- 3. Redistricting: the problem of partisan unfairness -- 4. What is a party's fair share? -- 5. The ranking protocol -- 6. The fair division redistricting protocol -- 7. Conclusion -- References -- When does approval voting make the "right choices"? -- 1. Introduction -- 2. Judging Multiple Proposals -- 3. State Dependence -- 4. Proposal Dependence -- 5. Other Kinds of Dependence -- 6. Follow-the-Leader -- 7. Applications to Politics -- 8. Relationship to the Condorcet Jury Theorem (CJT) -- 9. Conclusions -- References -- How indeterminate is sequential majority voting? A judgement aggregation perspective -- 1. Introduction -- 2. Preliminaries -- 3. Global indeterminacy -- 4. Full indeterminacy -- 5. Generalized Antichains -- 6. Condorcet entropy and almost full indeterminacy -- Conclusion -- Appendix: Proofs -- References -- Weighted voting, threshold functions, and zonotopes -- 1. Introduction -- 2. Hyperplane arrangements and zonotopes -- 3. The derived zonotope -- 4. Conclusions and future work -- 5. Acknowledgments -- References -- The Borda Count, the Kemeny Rule, and the Permutahedron -- 1. Introduction -- 2. Social Choice and Symmetry -- 3. Decompositions and Voting -- 4. Representations -- 5. Theorems and the Borda-Kemeny Spectrum -- 6. Looking Forward -- 7. Appendix -- References -- Double-interval societies -- 1. Introduction -- 2. Double- String Societies -- 3. Asymptotic approval ratios for double- string societies -- 4. A double-interval society lower bound -- 5. Modifying double- string societies -- 6. Conclusion and Open Questions -- References.

Voting for committees in agreeable societies -- 1. Introduction -- 2. Definitions -- 3. Votes Within a Ball -- 4. Concentric Voter Distributions -- 5. Main Theorem -- 6. Extensions -- References -- Selecting diverse committees with candidates from multiple categories -- 1. Introduction -- 2. Basic framework -- 3. Two categories, no slots -- 4. Three or more categories -- 5. Conclusion -- References -- Expanding the Robinson-Goforth system for 2×2 games -- 1. Introduction -- 2. The Robinson-Goforth system -- 3. Games with ties -- Acknowledgments -- References -- Cooperation in -player repeated games -- 1. Introduction -- 2. Sustaining Cooperation -- 3. Cooperation Inducement -- 4. Conclusion -- References -- The dynamics of consistent bankruptcy rules -- 1. Introduction -- 2. Literature Review -- 3. Bankruptcy Rules and Consistency -- 4. A Dynamic Approach to Solving the Bankruptcy Problem -- 5. A Closer Look at Pairwise Averaging Dynamics for TAL Rules -- 6. Conclusion and Future Directions -- Appendix: Proofs of Lemmas 5.4 and 5.5 -- Acknowledgments -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.