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The mathematics of voting and apport...

El-Helaly, Sherif.

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The mathematics of voting and apportionment = an introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The mathematics of voting and apportionment/ by Sherif El-Helaly.
Reminder of title:	an introduction /
Author:	El-Helaly, Sherif.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xv, 264 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Voting - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-030-14768-6
ISBN:	9783030147686

The mathematics of voting and apportionment = an introduction /
El-Helaly, Sherif.

The mathematics of voting and apportionmentan introduction /[electronic resource] :by Sherif El-Helaly. - Cham :Springer International Publishing :2019. - xv, 264 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

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.

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 Gardenfors' 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.".

ISBN: 9783030147686

Standard No.: 10.1007/978-3-030-14768-6doiSubjects--Topical Terms:

3411030
Voting
--Mathematics.

LC Class. No.: JF1001 / .E444 2019

Dewey Class. No.: 519

The mathematics of voting and apportionment = an introduction /
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100 1 $a El-Helaly, Sherif. $3 3411029
245 1 4 $a The mathematics of voting and apportionment $h [electronic resource] : $b an introduction / $c by Sherif El-Helaly.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xv, 264 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-4568
505 0 $a 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.
520 $a 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 Gardenfors' 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.".
650 0 $a Voting $x Mathematics. $3 3411030
650 1 4 $a Mathematics in the Humanities and Social Sciences. $3 1565599
650 2 4 $a Game Theory, Economics, Social and Behav. Sciences. $3 891103
650 2 4 $a Social Choice/Welfare Economics/Public Choice/Political Economy. $3 3383896
650 2 4 $a Electoral Politics. $3 2182104
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950 $a Mathematics and Statistics (Springer-11649)