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Mathematics of decisions, elections, and games / [edited by] Karl-Dieter Crisman and Michael A. Jones.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 624.Publication details: Providence : American Mathematical Society, c2014.Description: ix, 229 p. : illustrations ; 26 cmISBN:
  • 9780821898666 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Redistricting and district compactness / Carl Corcoran and Karen Saxe -- Fair division and redistricting / Zeph Landau and Francis Edward Su -- When does approval voting make the "Right Choices"? / Steven J. Brams and D. Marc Kilgour -- How indeterminate is sequential majority voting? A judgement aggregation perspective / Klaus Nehring and Marcus Pivato -- Weighted voting, threshold functions, and zonotopes / Catherine Stenson -- The Borda count, the Kemeny Rule, and the permutahedron / Karl-Dieter Crisman -- Double-interval societies / Maria Margaret Klawe, Kathryn L. Nyman, Jacob N. Scott, and Francis Edward Su -- Voting for committees in agreeable societies / Matt Davis, Michael E. Orrison, and Francis Edward Su -- Selecting diverse committees with candidates from multiple categories / Thomas C. Ratliff -- Expanding the Robinson-Goforth system for 2 x 2 games / Brian Hopkins -- Cooperation in n-player repeated games / Daniel T. Jessie and Donald G. Saari -- The dynamics of consistent bankruptcy rules / Michael A. Jones and Jennifer M. Wilson.
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.
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Includes bibliographical references.

Redistricting and district compactness / Carl Corcoran and Karen Saxe --
Fair division and redistricting / Zeph Landau and Francis Edward Su --
When does approval voting make the "Right Choices"? / Steven J. Brams and D. Marc Kilgour --
How indeterminate is sequential majority voting? A judgement aggregation perspective / Klaus Nehring and Marcus Pivato --
Weighted voting, threshold functions, and zonotopes / Catherine Stenson --
The Borda count, the Kemeny Rule, and the permutahedron / Karl-Dieter Crisman --
Double-interval societies / Maria Margaret Klawe, Kathryn L. Nyman, Jacob N. Scott, and Francis Edward Su --
Voting for committees in agreeable societies / Matt Davis, Michael E. Orrison, and Francis Edward Su --
Selecting diverse committees with candidates from multiple categories / Thomas C. Ratliff --
Expanding the Robinson-Goforth system for 2 x 2 games / Brian Hopkins --
Cooperation in n-player repeated games / Daniel T. Jessie and Donald G. Saari --
The dynamics of consistent bankruptcy rules / Michael A. Jones and Jennifer M. Wilson.

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.

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