Making Democracy Fair The Mathematics Of Voting And Apportionment

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Making Democracy Fair: The mathematics of voting and apportionment

Author : Michael de Villiers
Publisher : Lulu.com
ISBN 13 : 1300223561
Total Pages : 170 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Making Democracy Fair: The mathematics of voting and apportionment by : Michael de Villiers

Download or read book Making Democracy Fair: The mathematics of voting and apportionment written by Michael de Villiers and published by Lulu.com. This book was released on 2012-09-23 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do you know if an election is fair? Or if the result truly represents the choice of the people? In Making Democracy Fair students use elementary mathematical methods to explore different kinds of ballots, election decision procedures, and apportionment methods. In the first half of the book, students are introduced to a variety of alternatives to the "winner take all" strategy used in most elections. Determining which strategy is fairest is usually a very difficult question to answer, and many times the strategy chosen determines the winner. In the second part of the book, students investigate different methods of apportionment. How many representatives from each state will there be in the United States House of Representatives? How do countries using a proportional representation decide on the number of representatives from each political party to be seated in their government bodies?

Numbers Rule

Author : George Szpiro
Publisher : Princeton University Press
ISBN 13 : 0691209081
Total Pages : 240 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Numbers Rule by : George Szpiro

Download or read book Numbers Rule written by George Szpiro and published by Princeton University Press. This book was released on 2020-11-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author takes the general reader on a tour of the mathematical puzzles and paradoxes inherent in voting systems, such as the Alabama Paradox, in which an increase in the number of seats in the Congress could actually lead to a reduced number of representatives for a state, and the Condorcet Paradox, which demonstrates that the winner of elections featuring more than two candidates does not necessarily reflect majority preferences. Szpiro takes a roughly chronological approach to the topic, traveling from ancient Greece to the present and, in addition to offering explanations of the various mathematical conundrums of elections and voting, also offers biographical details on the mathematicians and other thinkers who thought about them, including Plato, Pliny the Younger, Pierre Simon Laplace, Thomas Jefferson, John von Neumann, and Kenneth Arrow.

The Mathematics of Voting and Apportionment

Author : Sherif El-Helaly
Publisher : Springer
ISBN 13 : 3030147681
Total Pages : 275 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Mathematics of Voting and Apportionment by : Sherif El-Helaly

Download or read book The Mathematics of Voting and Apportionment written by Sherif El-Helaly and published by Springer. This book was released on 2019-05-21 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.”

Mathematics to the Rescue of Democracy

Author : Paolo Serafini
Publisher : Springer Nature
ISBN 13 : 3030383687
Total Pages : 138 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Mathematics to the Rescue of Democracy by : Paolo Serafini

Download or read book Mathematics to the Rescue of Democracy written by Paolo Serafini and published by Springer Nature. This book was released on 2020-03-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains, in a straightforward way, the foundations upon which electoral techniques are based in order to shed new light on what we actually do when we vote. The intention is to highlight the fact that no matter how an electoral system has been designed, and regardless of the intentions of those who devised the system, there will be goals that are impossible to achieve but also opportunities for improving the situation in an informed way. While detailed descriptions of electoral systems are not provided, many references are made to current or past situations, both as examples and to underline particular problems and shortcomings. In addition, a new voting method that avoids the many paradoxes of voting theory is described in detail. While some knowledge of mathematics is required in order to gain the most from the book, every effort has been made to ensure that the subject matter is easily accessible for non-mathematicians, too. In short, this is a book for anyone who wants to understand the meaning of voting.

Mathematics and Democracy

Author : Steven J. Brams
Publisher : Princeton University Press
ISBN 13 : 1400835593
Total Pages : 390 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Mathematics and Democracy by : Steven J. Brams

Download or read book Mathematics and Democracy written by Steven J. Brams and published by Princeton University Press. This book was released on 2009-12-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In Mathematics and Democracy, Steven Brams, a leading authority in the use of mathematics to design decision-making processes, shows how social-choice and game theory could make political and social institutions more democratic. Using mathematical analysis, he develops rigorous new procedures that enable voters to better express themselves and that allow disputants to divide goods more fairly. One of the procedures that Brams proposes is "approval voting," which allows voters to vote for as many candidates as they like or consider acceptable. There is no ranking, and the candidate with the most votes wins. The voter no longer has to consider whether a vote for a preferred but less popular candidate might be wasted. In the same vein, Brams puts forward new, more equitable procedures for resolving disputes over divisible and indivisible goods.

Mathematics of Social Choice

Author : Christoph Borgers
Publisher : SIAM
ISBN 13 : 0898717620
Total Pages : 233 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematics of Social Choice by : Christoph Borgers

Download or read book Mathematics of Social Choice written by Christoph Borgers and published by SIAM. This book was released on 2010-01-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second part addresses compensation problems wherein an indivisible item must be assigned to one of several people who are equally entitled to ownership of the item, with monetary compensation paid to the others. The third part discusses the problem of sharing a divisible resource among several people. Mathematics of Social Choice can be used by undergraduates studying mathematics and students whose only mathematical background is elementary algebra. More advanced material can be skipped without any loss of continuity. The book can also serve as an easy introduction to topics such as the Gibbard-Satterthwaite theorem, Arrow's theorem, and fair division for readers with more mathematical background.

Making Democracy Count

Author : Ismar Volić
Publisher : Princeton University Press
ISBN 13 : 0691248826
Total Pages : 408 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Making Democracy Count by : Ismar Volić

Download or read book Making Democracy Count written by Ismar Volić and published by Princeton University Press. This book was released on 2024-04-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: How we can repair our democracy by rebuilding the mechanisms that power it What’s the best way to determine what most voters want when multiple candidates are running? What’s the fairest way to allocate legislative seats to different constituencies? What’s the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone. In this timely guide, Ismar Volić empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today’s divided public square. Examining our representative democracy using powerful clarifying concepts, Volić shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volić also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government. Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.

Fair Representation

Author : Michel L. Balinski
Publisher : Rowman & Littlefield
ISBN 13 : 9780815716341
Total Pages : 214 pages
Book Rating : 4.7/5 (163 download)

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Book Synopsis Fair Representation by : Michel L. Balinski

Download or read book Fair Representation written by Michel L. Balinski and published by Rowman & Littlefield. This book was released on 2010-12-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The issue of fair representation will take center stage as U.S. congressional districts are reapportioned based on the 2000 Census. Using U.S. history as a guide, the authors develop a theory of fair representation that establishes various principles for translating state populations—or vote totals of parties—into a fair allocation of congressional seats. They conclude that the current apportionment formula cheats the larger states in favor of the smaller, contrary to the intentions of the founding fathers and compromising the Supreme Court's "one man, one vote" rulings. Balinski and Young interweave the theoretical development with a rich historical account of controversies over representation, and show how many of these principles grew out of political contests in the course of United States history. The result is a work that is at once history, politics, and popular science. The book—updated with data from the 1980 and 1990 Census counts—vividly demonstrates that apportionment deals with the very substance of political power.

Math in Society

Author : David Lippman
Publisher :
ISBN 13 : 9781479276530
Total Pages : 0 pages
Book Rating : 4.2/5 (765 download)

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Book Synopsis Math in Society by : David Lippman

Download or read book Math in Society written by David Lippman and published by . This book was released on 2012-09-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

Is Democracy Fair?

Author : Leslie Johnson Nielsen
Publisher :
ISBN 13 : 9781559532778
Total Pages : 0 pages
Book Rating : 4.5/5 (327 download)

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Book Synopsis Is Democracy Fair? by : Leslie Johnson Nielsen

Download or read book Is Democracy Fair? written by Leslie Johnson Nielsen and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Social Justice: Resources for the College Classroom

Author : Gizem Karaali
Publisher : American Mathematical Soc.
ISBN 13 : 1470449269
Total Pages : 288 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics for Social Justice: Resources for the College Classroom by : Gizem Karaali

Download or read book Mathematics for Social Justice: Resources for the College Classroom written by Gizem Karaali and published by American Mathematical Soc.. This book was released on 2019-07-09 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Social Justice offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book begins with a series of essays from instructors experienced in integrating social justice themes into their pedagogy; these essays contain political and pedagogical motivations as well as nuts-and-bolts teaching advice. The heart of the book is a collection of fourteen classroom-tested modules featuring ready-to-use activities and investigations for the college mathematics classroom. The mathematical tools and techniques used are relevant to a wide variety of courses including college algebra, math for the liberal arts, calculus, differential equations, discrete mathematics, geometry, financial mathematics, and combinatorics. The social justice themes include human trafficking, income inequality, environmental justice, gerrymandering, voting methods, and access to education. The volume editors are leaders of the national movement to include social justice material into mathematics teaching. Gizem Karaali is Associate Professor of Mathematics at Pomona College. She is one of the founding editors of The Journal of Humanistic Mathematics, and an associate editor for The Mathematical Intelligencer and Numeracy ; she also serves on the editorial board of the MAA's Carus Mathematical Monographs. Lily Khadjavi is Associate Professor of Mathematics at Loyola Marymount University and is a past co-chair of the Infinite Possibilities Conference. She has served on the boards of Building Diversity in Science, the Barbara Jordan-Bayard Rustin Coalition, and the Harvard Gender and Sexuality Caucus.

Mathematics and Politics

Author : Alan D. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 0387776435
Total Pages : 378 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Mathematics and Politics by : Alan D. Taylor

Download or read book Mathematics and Politics written by Alan D. Taylor and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a text for an undergraduate mathematics course for nonmajors, Mathematics and Politics requires no prerequisites in either area while the underlying philosophy involves minimizing algebraic computations and focusing instead on some conceptual aspects of mathematics in the context of important real-world questions in political science. Five major topics are covered including a model of escalation, game theoretic models of international conflict, yes-no voting systems, political power, and social choice. Each topic is discussed in an introductory chapter and revisited in more depth in a later chapter. This new edition has added co-author, Allison Pacelli, and two new chapters on "Fairness" and "More Fairness." The examples and the exercises have been updated and enhanced throughout. Reviews from first edition: This book is well written and has much math of interest. While it is pitched at a non-math audience there is material here that will be new and interesting to the readers... -Sigact News For mathematicians, Taylor's book shows how the social sciences make use of mathematical thinking, in the form of axiomatic systems, and offers a chance to teach this kind of thinking to our students. - The College Mathematics Journal The writing is crisp and the sense of excitement about learning mathematics is seductive. The political conflict examples are well thought out and clear. -Michael C. Munger

Proportional Representation

Author : Friedrich Pukelsheim
Publisher : Springer
ISBN 13 : 3319647075
Total Pages : 350 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Proportional Representation by : Friedrich Pukelsheim

Download or read book Proportional Representation written by Friedrich Pukelsheim and published by Springer. This book was released on 2017-12-28 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an in-depth study of the translation of vote counts into seat numbers in proportional representation systems – an approach guided by practical needs. It also provides plenty of empirical instances illustrating the results. It analyzes in detail the 2014 elections to the European Parliament in the 28 member states, as well as the 2009 and 2013 elections to the German Bundestag. This second edition is a complete revision and expanded version of the first edition published in 2014, and many empirical election results that serve as examples have been updated. Further, a final chapter has been added assembling biographical sketches and authoritative quotes from individuals who pioneered the development of apportionment methodology. The mathematical exposition and the interrelations with political science and constitutional jurisprudence make this an apt resource for interdisciplinary courses and seminars on electoral systems and apportionment methods.

Some Adventures in Euclidean Geometry

Author : Michael de Villiers
Publisher : Dynamic Mathematics Learning
ISBN 13 : 0557102952
Total Pages : 221 pages
Book Rating : 4.5/5 (571 download)

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Book Synopsis Some Adventures in Euclidean Geometry by : Michael de Villiers

Download or read book Some Adventures in Euclidean Geometry written by Michael de Villiers and published by Dynamic Mathematics Learning. This book was released on 2009-09-08 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to actively involve the reader in the heuristic processes of conjecturing, discovering, formulating, classifying, defining, refuting, proving, etc. within the context of Euclidean geometry. The book deals with many interesting and beautiful geometric results, which have only been discovered during the past 300 years such as the Euler line, the theorems of Ceva, Napoleon, Morley, Miquel, Varignon, etc. Extensive attention is also given to the classification of the quadrilaterals from the symmetry of a side-angle duality. Many examples lend themselves excellently for exploration on computer with dynamic geometry programs such as Sketchpad. The book is addressed primarily to university or college lecturers involved in the under-graduate or in-service training of high school mathematics teachers, but may also interest teachers who are looking for enrichment material, and gifted high school mathematics pupils.

Teaching Mathematics for the 21st Century

Author : Linda Huetinck
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 612 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Teaching Mathematics for the 21st Century by : Linda Huetinck

Download or read book Teaching Mathematics for the 21st Century written by Linda Huetinck and published by Prentice Hall. This book was released on 2000 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: For courses in Mathematics Methods for the Secondary School. This is the first middle and secondary math methods text to focus on reform and the national standards. It prepares teachers for the challenge of assisting all students in reaching the highest level of mathematics according to their interest and realistic ambitions. It also provides contemporary methods of teaching mathematics-which facilitates successful instruction-with a strong understanding of the philosophy and psychology behind sound practices. Coverage includes methodology, curriculum materials, and use of technology, accompanied by many practical suggestions for implementation.

Mathematics and Democracy

Author : Bruno Simeone
Publisher : Springer Science & Business Media
ISBN 13 : 3540356053
Total Pages : 260 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Mathematics and Democracy by : Bruno Simeone

Download or read book Mathematics and Democracy written by Bruno Simeone and published by Springer Science & Business Media. This book was released on 2007-01-09 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, different quantitative approaches to the study of electoral systems have been developed: game-theoretic, decision-theoretic, statistical, probabilistic, combinatorial, geometric, and optimization ones. All the authors are prominent scholars from these disciplines. Quantitative approaches offer a powerful tool to detect inconsistencies or poor performance in actual systems. Applications to concrete settings such as EU, American Congress, regional, and committee voting are discussed.

The Oxford Handbook of Public Choice

Author : Roger D. Congleton
Publisher :
ISBN 13 : 0190469730
Total Pages : 985 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis The Oxford Handbook of Public Choice by : Roger D. Congleton

Download or read book The Oxford Handbook of Public Choice written by Roger D. Congleton and published by . This book was released on 2019 with total page 985 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This two-volume collection provides a comprehensive overview of the past seventy years of public choice research, written by experts in the fields surveyed. The individual chapters are more than simple surveys, but provide readers with both a sense of the progress made and puzzles that remain. Most are written with upper level undergraduate and graduate students in economics and political science in mind, but many are completely accessible to non-expert readers who are interested in Public Choice research. The two-volume set will be of broad interest to social scientists, policy analysts, and historians"--