Taylor, A: Simple Games - Desirability Relations, Trading, P

Alan D. Taylor|William S. Zwicker

ISBN 10: 0691001200 / ISBN 13: 9780691001203

Published by Princeton University Press, 1999

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Simple games are mathematical structures inspired by voting systems in which a single alternative. The mathematical study of the subject as a coherent subfield of finite combinatorics, this book includes introductory material, with an emphasis on Boolean su.

Seller Inventory # 594880848

Bibliographic Details

• Title: Taylor, A: Simple Games - Desirability Relations, Trading, P
• Publisher: Princeton University Press
• Publication Date: 1999
• Language: English
• ISBN 10: 0691001200
• ISBN 13: 9780691001203
• Binding: Hardcover
• Condition: New

About this title

Synopsis

Simple games are mathematical structures inspired by voting systems in which a single alternative, such as a bill, is pitted against the status quo. The first in-depth mathematical study of the subject as a coherent subfield of finite combinatorics--one with its own organized body of techniques and results--this book blends new theorems with some of the striking results from threshold logic, making all of it accessible to game theorists. Introductory material receives a fresh treatment, with an emphasis on Boolean subgames and the Rudin-Keisler order as unifying concepts. Advanced material focuses on the surprisingly wide variety of properties related to the weightedness of a game.


A desirability relation orders the individuals or coalitions of a game according to their influence in the corresponding voting system. As Taylor and Zwicker show, acyclicity of such a relation approximates weightedness--the more sensitive the relation, the closer the approximation. A trade is an exchange of players among coalitions, and robustness under such trades is equivalent to weightedness of the game. Robustness under trades that fit some restrictive exchange pattern typically characterizes a wider class of simple games--for example, games for which some particular desirability order is acyclic. Finally, one can often describe these wider classes of simple games by weakening the total additivity of a weighting to obtain what is called a pseudoweighting. In providing such uniform explanations for many of the structural properties of simple games, this book showcases numerous new techniques and results.

About the Author

Alan D. Taylor is the Marie Louise Bailey Professor of Mathematics at Union College. William S. Zwicker is Professor of Mathematics at Union College. Both have taught at Union for twenty-four years; their research has been in the areas of combinatorial set theory and applications of mathematics to political science, including social choice theory, fair division, and game theory.