**Contemporary Mathematics**

Volume: 624;
2014;
229 pp;
Softcover

MSC: Primary 91;

Print ISBN: 978-0-8218-9866-6

Product Code: CONM/624

List Price: $91.00

Individual Member Price: $72.80

**Electronic ISBN: 978-1-4704-1930-1
Product Code: CONM/624.E**

List Price: $91.00

Individual Member Price: $72.80

# The Mathematics of Decisions, Elections, and Games

Share this page *Edited by *
*Karl-Dieter Crisman; Michael A. Jones*

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, and January 11–12, 2013, in San Diego,
CA.

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.

#### Table of Contents

# Table of Contents

## The Mathematics of Decisions, Elections, and Games

- Preface vii8 free
- Redistricting and district compactness 112 free
- Fair division and redistricting 1728
- When does approval voting make the “right choices”? 3748
- How indeterminate is sequential majority voting? A judgement aggregation perspective 5566
- Weighted voting, threshold functions, and zonotopes 89100
- The Borda Count, the Kemeny Rule, and the Permutahedron 101112
- Double-interval societies 135146
- Voting for committees in agreeable societies 147158
- Selecting diverse committees with candidates from multiple categories 159170
- Expanding the Robinson-Goforth system for 2×2 games 177188
- Cooperation in 𝑛-player repeated games 189200
- The dynamics of consistent bankruptcy rules 207218
- 1. Introduction 207218
- 2. Literature Review 208219
- 3. Bankruptcy Rules and Consistency 211222
- 4. A Dynamic Approach to Solving the Bankruptcy Problem 216227
- 5. A Closer Look at Pairwise Averaging Dynamics for TAL Rules 220231
- 6. Conclusion and Future Directions 226237
- Appendix: Proofs of Lemmas 5.4 and 5.5 227238
- Acknowledgments 227238
- References 227238

#### Readership

Graduate students and research mathematicians interested in decision making, voting, and games.