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Compact Textbooks in Mathematics

The Mathematics of Voting and Apportionment

An Introduction

Authors: El-Helaly, Sherif

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  • 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
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書籍の購入

イーブック ¥3,930
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-14768-6
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ソフトカバー ¥4,913
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-14767-9
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
この教本について

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics.
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 that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”

著者について

Sherif El-Helaly is an associate professor at The Catholic University of America in Washington, DC, where he has been teaching a course on mathematical topics in the social sciences for twenty years.

Table of contents (3 chapters)

Table of contents (3 chapters)

書籍の購入

イーブック ¥3,930
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-14768-6
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF, EPUB
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
  • ご購入後、すぐにダウンロードしていただけます。
ソフトカバー ¥4,913
価格の適用国: Japan (日本円価格は個人のお客様のみ有効) (小計)
  • ISBN 978-3-030-14767-9
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
  • Usually dispatched within 3 to 5 business days.
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書誌情報

Bibliographic Information
Book Title
The Mathematics of Voting and Apportionment
Book Subtitle
An Introduction
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
イーブック ISBN
978-3-030-14768-6
DOI
10.1007/978-3-030-14768-6
ソフトカバー ISBN
978-3-030-14767-9
Series ISSN
2296-4568
Edition Number
1
Number of Pages
XV, 264
Number of Illustrations
25 b/w illustrations, 2 illustrations in colour
Topics