2nd Edition

The Mathematics of Politics

    478 Pages 14 B/W Illustrations
    by CRC Press

    478 Pages 14 B/W Illustrations
    by CRC Press

    It is because mathematics is often misunderstood, it is commonly



    believed it has nothing to say about politics. The high school



    experience with mathematics, for so many the lasting impression



    of the subject, suggests that mathematics is the study of numbers,



    operations, formulas, and manipulations of symbols. Those



    believing 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 reasoning



    about politics. In the search for ideal ways to make certain kinds



    of decisions, a lot of wasted effort can be averted if mathematics can determine that



    finding such an ideal is actually impossible in the first place.





    In the first three parts of this book, we address the following three



    political 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 and



    uncertainty?





    In the fourth and final part of this book, we examine the Electoral



    College system that is used in the United States to select a president.



    There we bring together ideas that are introduced in each of the three



    earlier parts of the book.

    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 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



    III CONFLICT



    Strategies and Outcomes



    Chance and Expectation



    Solving Zero-Sum Games



    Conflict and Cooperation



    Nash Equilibria



    The Prisoner’s Dilemma



    Notes on Part III



    IV THE ELECTORAL COLLEGE



    Weighted Voting



    Whose Advantage?



    Notes on Part IV



    Solutions to Odd-Numbered Exercises and Problems

    Biography

    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.