This book focuses on mathematical reasoning about politics. People commonly believe mathematics has nothing to say about politics. The high school experience suggests mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those who, from this experience, conclude mathematics has no relevance to politics will not find much in this book they regard as mathematics. A lot of wasted effort can be averted if mathematics is used to determine whether some decisions are actually impossible in the first place. Is it possible to create methods to vote, methods to…mehr
This book focuses on mathematical reasoning about politics. People commonly believe mathematics has nothing to say about politics. The high school experience suggests mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those who, from this experience, conclude mathematics has no relevance to politics will not find much in this book they regard as mathematics. A lot of wasted effort can be averted if mathematics is used to determine whether some decisions are actually impossible in the first place. Is it possible to create methods to vote, methods to apportion, and methods to make decisions in a satisfactory way? This is where mathematics meets politics.
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.
Inhaltsangabe
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
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
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