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


    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


    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


    Strategies and Outcomes

    Chance and Expectation

    Solving Zero-Sum Games

    Conflict and Cooperation

    Nash Equilibria

    The Prisoner’s Dilemma

    Notes on Part III


    Weighted Voting

    Whose Advantage?

    Notes on Part IV

    Solutions to Odd-Numbered Exercises and Problems


    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.