MATHEMATICS AND POLITICS: .

by Alan D. Taylor

interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. My experience at Union College has been that there is a real advan­ tage in having students enter the course knowing thatvirtually all the applications will focus on a single discipline-in this case, political science. The level ofpresentation assumes no college-level mathematicalor social science prerequisites. The philosophy underlying the approach we have taken in this book is based on the sense that we (mathemati­ cians)havetendedtomaketwoerrorsinteachingnonsciencestudents: wehaveoverestimatedtheircomfortwithcomputationalmaterial,and we have underestimated their ability to handle conceptual material. Thus, while there is very little algebra (and certainly no calculus) in our presentation, we have included numerous logical arguments that students in the humanitiesand the socialscienceswill find accessible, but not trivial. The book contains five main topics: a m.odel of escalation, game­ theoretic models of international conflict, yes-no voting systems, political power, and social choice. The first partofthe text is made up of a single chapter devoted to each topic. The second part of the text revisits each topic, again with a single chapter devoted to each. The organizationofthe bookisbasedonpedagogicalconsiderations, with the material becoming somewhat more sophisticated as one moves through the ten chapters. On the other hand, within any given chap­ terthere is little reliance on material from earlierchapters, except for those devoted to the same topic.

Genres: Mathematics, Nonfiction, Politics

284 pages, Paperback

First published January 1, 1995

Reviews

[Isaac · Rating 4 out of 5]

This is an excellent text, written by Alan Taylor -- a well known in the area of fair division research -- that most other undergraduate texts on similar topics seem to base themselves on. The second edition, written in conjunction with Taylor's former student Allison Pacelli, extends the first edition by adding material on the topic of fairness and restructuring the existing material on voting as social choice, voting in yes-no situations, power indices, game theory and escalation situation like auctions. The book covers a lot of ground and tries at all times to be accessible to those not used to mathematical formalism. On the whole this book does great job of focusing on the logic behind mathematics results related to social situations.

I have two criticisms. Firstly, the structural choice of having one chapter on a particular topic - say social choice - early in the book and then having a follow-up chapter much later in the book (i.e. several chapters later) is annoying if you are wanting to follow a particular theme. I do note that Taylor & Pacelli are not alone here Smith's Chance, Strategy, and Choice: An Introduction to the Mathematics of Games and Elections does that too.

Secondly, I do wish the book was a bit more mathematical in places - the text feel a bit "loose" at times. However, this flies in the face of the authors' stated goals and target audience so I assume I'm not in that group and should just live with it.

Highly recommended.

[Ron Me]

I like this book way better than the last one. Although I'm mystified why he assumes the reader is unfamiliar with "mod" and thus spends half a page doing subtractions (sic!), but IS assumed to be familiar with factorials.

[Bob Stocker · Rating 4 out of 5]

Mathematics and Politics by Alan D. Taylor is a textbook designed for a college course offered to undergraduate non-mathematics majors. Five major political topics are covered: escalation, models for international conflict, yes-no voting (i.e. voting with only two alternatives), measures of political power, and social choice (i.e. voting with three or more alternatives). The text is a mix of discussion, real-world examples, theorems and proofs. Generally, the writing is clear and proofs are complete (at least complete enough to satisfy a non-mathematician like myself). There's an abundance of diagrams and very little algebra.

Although I found the material interesting, I didn't make a concerted effort to master it. I didn't study proofs carefully enough to be able to reproduce them. Each of the ten chapters is followed by numerous exercises all of which I left undone. However, I did at times marvel at some of the mathematical conclusions. Perhaps someday I'll work through the material carefully enough to understand these conclusions in greater depth. At the moment I'm ready to read a novel.

[vasily · Rating 5 out of 5]

Great book! Both mathematically non-trivial and easy to read -- a great combination.

[AMARDEEP SAINI]

good