The Mathematics of Voting and Apportionment An Introduction /

• Main Author: El-Helaly, Sherif (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Compact Textbooks in Mathematics,
• Subjects: Mathematics.; Social sciences.; Game theory.; Welfare economics.; Elections.; Mathematics in the Humanities and Social Sciences.; Game Theory, Economics, Social and Behav. Sciences.; Social Choice/Welfare Economics/Public Choice/Political Economy.; Electoral Politics.

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,...

Table of Contents:

• 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.