The Mathematics of Decisions, Elections, and Games
About this Title
Karl-Dieter Crisman, Gordon College, Wenham, MA and Michael A. Jones, Mathematical Reviews, Ann Arbor, MI, Editors
Publication: Contemporary Mathematics
Publication Year 2014: Volume 624
ISBNs: 978-0-8218-9866-6 (print); 978-1-4704-1930-1 (online)
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.
Graduate students and research mathematicians interested in decision making, voting, and games.
Table of Contents
- Carl Corcoran and Karen Saxe – Redistricting and district compactness
- Zeph Landau and Francis Edward Su – Fair division and redistricting
- Steven J. Brams and D. Marc Kilgour – When does approval voting make the “right choices”?
- Klaus Nehring and Marcus Pivato – How indeterminate is sequential majority voting? A judgement aggregation perspective
- Catherine Stenson – Weighted voting, threshold functions, and zonotopes
- Karl-Dieter Crisman – The Borda Count, the Kemeny Rule, and the Permutahedron
- Maria Margaret Klawe, Kathryn L. Nyman, Jacob N. Scott and Francis Edward Su – Double-interval societies
- Matt Davis, Michael E. Orrison and Francis Edward Su – Voting for committees in agreeable societies
- Thomas C. Ratliff – Selecting diverse committees with candidates from multiple categories
- Brian Hopkins – Expanding the Robinson-Goforth system for $2 \times 2$ games
- Daniel T. Jessie and Donald G. Saari – Cooperation in $n$-player repeated games
- Michael A. Jones and Jennifer M. Wilson – The dynamics of consistent bankruptcy rules