Overview
- Provides students with an accessible overview of the mathematical concepts central to voting systems
- Allows readers to engage with the material in a variety of ways, with chapters that can be approached in any order
- Includes a chapter on the mathematics of apportionment, a topic not always covered in adequate detail
Part of the book series: Compact Textbooks in Mathematics (CTM)
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About this book
The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types.
The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications.
No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity thatenables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”
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Table of contents (3 chapters)
Reviews
“As intended audience the author mentions students in economics, political science, philosophy and (applied) mathematics, but I think the book is also to be recommended to law students … . I like to suggest to include this topic in a next edition of this admirable book.” (H. C. M. de Swart, zbMATH 1426.91001, 2020)
“This is a nicely written book, with clear explanations that are supported by a number of useful, fully worked out, examples. … more appropriate audience would be math majors in a proof-based course who already have some experience in reading precisely stated definitions and statements of theorems, and a willingness to track through the details of a proof.” (Mark Hunacek, MAA Reviews, August 11, 2019)
“This book, is a textbook that is clearly addressing an audience of social science students, in particular in the US … . It is not only a textbook for his students, but it brings together a lot of material that is not easily found in this compact form and as such it will be of interest to any politician or anyone who is generally interested in the subject.” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, July 01, 2019)
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Bibliographic Information
Book Title: The Mathematics of Voting and Apportionment
Book Subtitle: An Introduction
Authors: Sherif El-Helaly
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-030-14768-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-14767-9Published: 04 June 2019
eBook ISBN: 978-3-030-14768-6Published: 21 May 2019
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XV, 264
Number of Illustrations: 25 b/w illustrations, 2 illustrations in colour
Topics: Mathematics in the Humanities and Social Sciences, Game Theory, Economics, Social and Behav. Sciences, Social Choice/Welfare Economics/Public Choice/Political Economy, Electoral Politics