The mathematics of decisions, elections, and games / Karl-Dieter Crisman, Michael A. Jones, editors.

Format:

Book

Contributor:

Crisman, Karl-Dieter, 1975- editor.

Jones, Michael A., 1967- editor.

Series:

Contemporary mathematics (American Mathematical Society) ; 624.

Contemporary Mathematics, 1098-3627 ; 624

Language:

English

Subjects (All):

Game theory.

Statistical decision.

Probabilities.

Physical Description:

1 online resource (229 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

This volume contains the proceedings of two AMS Special Sessions on The Mathematics of Decisions, Elections, and Games, held January 4, 2012, in Boston, MA, USA and January 11-12, 2013, in San Diego, CA, USA. Decision theory, voting theory, and game theory are three intertwined areas of mathematics that involve making optimal decisions under different contexts. Although these areas include their own mathematical results, much of the recent research in these areas involves developing and applying new perspectives from their intersection with other branches of mathematics, such as algebra, representation theory, combinatorics, convex geometry, dynamical systems, etc. The papers in this volume highlight and exploit the mathematical structure of decisions, elections, and games to model and to analyze problems from the social sciences.

Contents:

""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""

""4. A Dynamic Approach to Solving the Bankruptcy Problem""

Notes:

"AMS Special Sessions on The Mathematics of Decisions, Elections, and Games, January 4, 2012, Boston, MA, Janaury 11-12, 2013, San Diego, CA."--Cover.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-1930-0