Mathematics of Politics

AvE. Arthur Robinson Jr.,Daniel H. Ullman

Inbunden, Engelska, 2016

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Beskrivning

It is because mathematics is often misunderstood, it is commonlybelieved it has nothing to say about politics. The high schoolexperience with mathematics, for so many the lasting impressionof the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Thosebelieving this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoningabout politics. In the search for ideal ways to make certain kindsof decisions, a lot of wasted effort can be averted if mathematics can determine thatfinding such an ideal is actually impossible in the first place.In the first three parts of this book, we address the following threepolitical questions:(1) Is there a good way to choose winners of elections?(2) Is there a good way to apportion congressional seats?(3) Is there a good way to make decisions in situations of conflict anduncertainty?In the fourth and final part of this book, we examine the ElectoralCollege system that is used in the United States to select a president.There we bring together ideas that are introduced in each of the threeearlier parts of the book.

Produktinformation

Utgivningsdatum:2016-11-16
Mått:152 x 229 x 31 mm
Vikt:1 700 g
Format:Inbunden
Språk:Engelska
Antal sidor:478
Upplaga:2
Förlag:Taylor & Francis Inc
ISBN:9781498798860

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Mer om författaren

E. Arthur Robinson, Jr. is a Professor of Mathematics a Professor of mathematics at the George Washington University, where he has been since 1987. Like his coauthor, he was once the department chair. His current research is primarily in the area of dynamical systems theory and discrete geometry. Besides teaching the Mathematics and Politics course, he is teaching a course on Math and Art for the students of the Corcoran School the Arts and Design.Daniel H. Ullman is a Professor of Mathematics at the George Washington University, where he has been since 1985. He holds a Ph.D. from Berkeley and an A.B. from Harvard. He served as chair of the department of mathematics at GW from 2001 to 2006, as the American Mathematical Society Congressional Fellow from 2006 to 2007, and as Associate Dean for Undergraduate Studies in the arts and sciences at GW from 2011 to 2015. He has been an Associate Editor of the American Mathematical Monthly since 1997. He enjoys playing piano, soccer, and Scrabble.

Innehållsförteckning

I VOTING Two Candidates Social Choice Functions Criteria for Social Choice Which Methods Are Good?Arrow’s Theorem Variations on a Theme Notes on Part I II: APPORTIONMENT Hamilton’s MethodDivisor Methods Criteria and Impossibility The Method of Balinski and Young Deciding among Divisor Methods History of Apportionment in the United StatesNotes on Part II III CONFLICTStrategies and OutcomesChance and Expectation Solving Zero-Sum Games Conflict and CooperationNash Equilibria The Prisoner’s DilemmaNotes on Part III IV THE ELECTORAL COLLEGEWeighted Voting Whose Advantage?Notes on Part IV Solutions to Odd-Numbered Exercises and Problems