The Mathematics of Voting and Apportionment

Inhaltsverzeichnis

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.

The Mathematics of Voting and Apportionment

An Introduction

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The Mathematics of Voting and Apportionment

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Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

04.06.2019

Verlag

Springer

Seitenzahl

264

Maße (L/B/H)

23,5/15,5/1,5 cm

Beschreibung

Rezension

“The mathematics of voting and apportionment is a well-written, thorough introduction to social choice and social welfare theory. … This book is suitable as the main text for a one-semester introduction to voting theory and apportionment. I would also recommend this book to anyone interested in independently studying these topics. It is a clearly written, entry-level text into voting theory and apportionment.” (Brittany Shelton, Mathematical Reviews, February, 2020)

“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)

Details

Einband

Taschenbuch

Erscheinungsdatum

04.06.2019

Verlag

Springer

Seitenzahl

264

Maße (L/B/H)

23,5/15,5/1,5 cm

Gewicht

488 g

Auflage

2019

Sprache

Englisch

ISBN

978-3-030-14767-9

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  • The Mathematics of Voting and Apportionment
  • 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.