The Mathematics Of Voting And Elections
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The Mathematics Of Voting And Elections
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Author : Jonathan K. Hodge
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Mathematics Of Voting And Elections written by Jonathan K. Hodge 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 2005 with Mathematics categories.
The Mathematics of Voting and Elections: A Hands-on Approach will help you discover answers to these and many other questions. Easily accessible to anyone interested in the subject, the book requires virtually no prior mathematical experience beyond basic arithmetic, and includes numerous examples and discussions regarding actual elections from politics and popular culture.
The Mathematics Of Elections And Voting
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Author : W.D. Wallis
language : en
Publisher: Springer
Release Date : 2014-10-08
The Mathematics Of Elections And Voting written by W.D. Wallis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-08 with Mathematics categories.
This title takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness, approval voting, ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcet’s Principle and Arrow’s Theorem of conditions in electoral fairness. Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees. In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life. Few books have studied voting and elections from a more formal mathematical viewpoint. This text will be useful to those who teach lower level courses or special topics courses and aims to inspire students to understand the more advanced mathematics of the topic. The exercises in this text are ideal for upper undergraduate and early graduate students, as well as those with a keen interest in the mathematics behind voting and elections.
The Mathematics Of Voting And Apportionment
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Author : Sherif El-Helaly
language : en
Publisher: Springer
Release Date : 2019-05-21
The Mathematics Of Voting And Apportionment written by Sherif El-Helaly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-21 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.”
The Mathematics Of Politics
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Author : E. Arthur Robinson
language : en
Publisher: CRC Press
Release Date : 2016-11-18
The Mathematics Of Politics written by E. Arthur Robinson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-18 with Mathematics categories.
It is because mathematics is often misunderstood, it is commonly believed it has nothing to say about politics. The high school experience with mathematics, for so many the lasting impression of the subject, suggests that mathematics is the study of numbers, operations, formulas, and manipulations of symbols. Those believing this is the extent of mathematics might conclude mathematics has no relevance to politics. This book counters this impression. The second edition of this popular book focuses on mathematical reasoning about politics. In the search for ideal ways to make certain kinds of decisions, a lot of wasted effort can be averted if mathematics can determine that finding such an ideal is actually impossible in the first place. In the first three parts of this book, we address the following three political questions: (1) Is there a good way to choose winners of elections? (2) Is there a good way to apportion congressional seats? (3) Is there a good way to make decisions in situations of conflict and uncertainty? In the fourth and final part of this book, we examine the Electoral College system that is used in the United States to select a president. There we bring together ideas that are introduced in each of the three earlier parts of the book.
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?
An Introduction To The Math Of Voting Methods
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Author : Brendan W Sullivan
language : en
Publisher:
Release Date : 2022-09
An Introduction To The Math Of Voting Methods written by Brendan W Sullivan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09 with Mathematics categories.
Some modern political discussions are focused on electoral reform and the mechanics of democracy. For instance, Maine and Alaska recently adopted new procedures for statewide elections that involve Ranked Choice Voting, while a similar ballot measure in Massachusetts was only narrowly defeated. Meanwhile, countries all over the world use other voting methods with runoffs or scores. It's important for people to be aware of how different voting methods work in practice so that we can have productive debates about which to use in various situations. Accordingly, this book will teach you about a variety of voting methods through concrete examples and clear explanations. Each chapter illustrates a different type of voting method using basic definitions, real-world examples, a list of pros and cons, and detailed practice problems with solutions. No prior mathematical or political knowledge is assumed. In fact, the prose is designed for a wide audience, making this book ideal for a general education mathematics course or anyone else who is curious to learn about different methods of voting.
Chaotic Elections
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Author : Donald Saari
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-04-03
Chaotic Elections written by Donald Saari 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 2001-04-03 with Political Science categories.
What does the 2000 U.S. presidential election have in common with selecting a textbook for a calculus course in your department? Was Ralph Nader's influence on the election of George W. Bush greater than the now-famous chads? In Chaotic Elections!, Don Saari analyzes these questions, placing them in the larger context of voting systems in general. His analysis shows that the fundamental problems with the 2000 presidential election are not with the courts, recounts, or defective ballots, but are caused by the very way Americans vote for president. This expository book shows how mathematics can help to identify and characterize a disturbingly large number of paradoxical situations that result from the choice of a voting procedure. Moreover, rather than being able to dismiss them as anomalies, the likelihood of a dubious election result is surprisingly large. These consequences indicate that election outcomes--whether for president, the site of the next Olympics, the chair of a university department, or a prize winner--can differ from what the voters really wanted. They show that by using an inadequate voting procedure, we can, inadvertently, choose badly. To add to the difficulties, it turns out that the mathematical structures of voting admit several strategic opportunities, which are described. Finally, mathematics also helps identify positive results: By using mathematical symmetries, we can identify what the phrase ``what the voters really want'' might mean and obtain a unique voting method that satisfies these conditions. Saari's book should be required reading for anyone who wants to understand not only what happened in the presidential election of 2000, but also how we can avoid similar problems from appearing anytime any group is making a choice using a voting procedure. Reading this book requires little more than high school mathematics and an interest in how the apparently simple situation of voting can lead to surprising paradoxes.
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.
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.
Numbers Rule
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Author : George Szpiro
language : en
Publisher: Princeton University Press
Release Date : 2020-11-03
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 2020-11-03 with History categories.
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.