Making Democracy Fair The Mathematics Of Voting And Apportionment
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Making Democracy Fair The Mathematics Of Voting And Apportionment
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Author : Michael de Villiers
language : en
Publisher: Lulu.com
Release Date : 2012-09-23
Making Democracy Fair The Mathematics Of Voting And Apportionment written by Michael de Villiers and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-23 with Education categories.
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?
Making Democracy Count
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Author : Ismar Volić
language : en
Publisher: Princeton University Press
Release Date : 2024-04-02
Making Democracy Count written by Ismar Volić and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-02 with Political Science categories.
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.
Numbers Rule
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Author : George Szpiro
language : en
Publisher: Princeton University Press
Release Date : 2010-03-15
Numbers Rule written by George Szpiro and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-15 with Mathematics categories.
A lively history of the peculiar math of voting Since the very birth of democracy in ancient Greece, the simple act of voting has given rise to mathematical paradoxes that have puzzled some of the greatest philosophers, statesmen, and mathematicians. Numbers Rule traces the epic quest by these thinkers to create a more perfect democracy and adapt to the ever-changing demands that each new generation places on our democratic institutions. In a sweeping narrative that combines history, biography, and mathematics, George Szpiro details the fascinating lives and big ideas of great minds such as Plato, Pliny the Younger, Ramon Llull, Pierre Simon Laplace, Thomas Jefferson, Alexander Hamilton, John von Neumann, and Kenneth Arrow, among many others. Each chapter in this riveting book tells the story of one or more of these visionaries and the problem they sought to overcome, like the Marquis de Condorcet, the eighteenth-century French nobleman who demonstrated that a majority vote in an election might not necessarily result in a clear winner. Szpiro takes readers from ancient Greece and Rome to medieval Europe, from the founding of the American republic and the French Revolution to today's high-stakes elective politics. He explains how mathematical paradoxes and enigmas can crop up in virtually any voting arena, from electing a class president, a pope, or prime minister to the apportionment of seats in Congress. Numbers Rule describes the trials and triumphs of the thinkers down through the ages who have dared the odds in pursuit of a just and equitable democracy.
Mathematics And Democracy
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Author : Steven J. Brams
language : en
Publisher: Princeton University Press
Release Date : 2009-12-02
Mathematics And Democracy written by Steven J. Brams and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Science categories.
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 For Social Justice Resources For The College Classroom
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Author : Gizem Karaali
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-09
Mathematics For Social Justice Resources For The College Classroom written by Gizem Karaali and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-09 with Juvenile Nonfiction categories.
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.
The Mathematics Of Voting And Apportionment
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Author : Sherif El-Helaly
language : en
Publisher: Birkhäuser
Release Date : 2019-06-04
The Mathematics Of Voting And Apportionment written by Sherif El-Helaly and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-04 with Mathematics categories.
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 For Humanists Revealing The Math Around Us
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-05-16
Mathematics For Humanists Revealing The Math Around Us written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-16 with Mathematics categories.
Mathematics is all around us, yet many people feel intimidated by it. This book is for those people. We will explore the many ways that mathematics is used in our everyday lives, from the patterns in nature to the algorithms that power our computers. We will also learn about the history of mathematics, from the ancient Greeks to the modern day, and meet some of the brilliant minds who have helped to shape this fascinating field. But this book is not just about the history and applications of mathematics. It is also about the beauty and elegance of the subject. We will explore the mathematical principles that underlie our world, from the golden ratio to the concept of infinity. We will also learn about the many ways that mathematics can be used to create art, music, and other forms of beauty. This book is for anyone who wants to learn more about mathematics, regardless of their background or skill level. We will start with the basics and gradually build up to more complex concepts. By the end of the book, you will have a new appreciation for the beauty and power of mathematics. Whether you are a math lover or a math hater, this book is for you. We will show you that mathematics is not just a dry and abstract subject, but a vibrant and dynamic field that is essential for understanding the world around us. With clear explanations, engaging stories, and beautiful illustrations, this book will make mathematics accessible to everyone. So open your mind and prepare to be amazed by the world of mathematics. If you like this book, write a review on google books!
Mathematics To The Rescue Of Democracy
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Author : Paolo Serafini
language : en
Publisher: Springer Nature
Release Date : 2020-03-02
Mathematics To The Rescue Of Democracy written by Paolo Serafini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Mathematics categories.
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.
Teaching Mathematics For The 21st Century
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Author : Linda Huetinck
language : en
Publisher: Prentice Hall
Release Date : 2000
Teaching Mathematics For The 21st Century written by Linda Huetinck and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Education categories.
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
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Author : Bruno Simeone
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-09
Mathematics And Democracy written by Bruno Simeone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-09 with Business & Economics categories.
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.