The mathematics of voting and apportionment : an introduction / Sherif El-Helaly.
El-Helaly, Sherif, author.
2019
JF1001 .E44 2019
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Title
The mathematics of voting and apportionment : an introduction / Sherif El-Helaly.
Author
El-Helaly, Sherif, author.
ISBN
9783030147686 (electronic book)
3030147681 (electronic book)
3030147673
9783030147679
DOI
https://doi.org/10.1007/978-3-030-14
Published
Cham, Switzerland : Birkhäuser, [2019]
Language
English
Description
1 online resource : illustrations
Item Number
10.1007/978-3-030-14 doi
Call Number
JF1001 .E44 2019
Dewey Decimal Classification
324.650151
Summary
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 texts 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 Arrows theorems on dictatorship, Gibbards 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, an d intuitively grasp logical notions such as "contrapositive" and "counterexample."
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from digital title page (viewed on June 28, 2019).
Series
Compact textbooks in mathematics.
Available in Other Form
Print version 9783030147679
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Chapter 1: Social Choice
Introduction
Elimination Procedures
Condorcet Ideas and Related Procedures
Scoring Procedures: Borda Count
A Glimpse into Social Welfare Theory
Social Choice Procedures: Indifference and Ties Allowed
Manipulability of Social Choice Procedures: Indifference and Ties Allowed
Exercises
Chapter 2: Yes-No Voting
Introduction
Quantification of Power in a Yes-No Voting System
Some Combinatorics
Banzhaf and Shapley-Shubik Indices in One View
Weightable Yes-No Voting Systems
Exercises
Chapter 3: Apportionment
Introduction
Axioms of Apportionment
Quota Procedures
Divisor Procedures
Equity Criteria
Apportionment Paradoxes
Applications of Priority Formulas
Exercises.

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