What Ralph Nader's spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Dean's method. How the US tried to use game theory to win the Cold War, and why it didn't work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics.
A Mathematical Look at Politics is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions, lemmas, theorems, and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results, prove them, and draw conclusions about specific examples. Tying the liberal arts classroom to real-world mathematical applications, this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.
By:
E. Arthur Robinson Jr.,
Daniel H. Ullman
Imprint: CRC Press Inc
Country of Publication: United States
Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 30mm
Weight: 839g
ISBN: 9781439819838
ISBN 10: 1439819831
Pages: 478
Publication Date: 09 December 2010
Audience:
College/higher education
,
General/trade
,
Primary
,
ELT Advanced
Format: Hardback
Publisher's Status: Active
Preface, for the Student. Preface, for the Instructor Voting Two Candidates. Social Choice Functions. Criteria for Social Choice. Which Methods are Good? Arrow's Theorem. Variations on the Theme. Notes on Part I Apportionment Hamilton's Method. Divisor Methods. Criteria and Impossibility. The Method of Balinski and Young. Deciding Among Divisor Methods. History of Apportionment in the United States. Notes on Part II. Conflict Strategies and Outcomes. Chance and Expectation. Solving Zero-Sum Games. Conflict and Cooperation. Nash Equilibria. The Prisoner's Dilemma. Notes on Part III The Electoral College Weighted Voting. Whose Advantage? Notes on Part IV. Solutions to Odd-Numbered Exercises and Problems. Bibliography. Index
E. Arthur Robinson Jr., Daniel H. Ullman
Reviews for A Mathematical Look at Politics
The book finds a nice compromise between formality and accessibility. The authors take care to build from examples, isolate what is important, and generalize into theorems. It is expected that the reader has only limited mathematical experience, so much effort is put toward making very clear what is and is not being said. ... The exercises that close each chapter are interesting and often quite challenging ... Topics are introduced and motivated thoughtfully. Definitions are clear, and the authors take the time to explain why they need to be with well-chosen examples. When the proofs come (and they do come), they are set up properly. ... The book has plenty of uses other than as a textbook. Instructors teaching a broader liberal arts mathematics course could use it to add depth to these topics or craft supplemental readings and projects. Students of mathematics or politics will find independent study opportunities here, and mathematicians from other areas will find this an enjoyable introduction. This is a very thoughtfully written text that should be made available to anyone with an interest in learning or teaching this topic. -MAA Reviews, July 2011
