Basic Geometry of Voting

Book Description

A surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a new profile decomposition quickly resolves two centuries old controversies of Condorcet and Borda, demonstrates, that the rankings of pairwise and other methods differ because they rely on different information, casts series doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow`s Theorem predictable, and simplifies the construction of examples. The geometry unifies seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court.

Customer Reviews:

learn mathematics of voting.......2005-09-11

Great book! Interesting new theory developed to visualize voting systems. Can be technical - best used in conjunction with "Chaotic Elections", which is more of an overview. It is nice to see an application of mathematics that doesn't require a huge amount of mathematical training - just some familiarity with vectors and parametrizations of lines and planes. Accessible to many people interested in how math can be used to model voting systems, from high school onwards.

The most important work since Arrow.......2001-01-19

This book is the most important work in social choice theory since Arrow's (1963) "Social Choice and Individual Values". Professor Saari (now at UC Irvine) used this book in an advanced graduate course I took in Fall 2000, and he covered nearly the entire book in a ten week course (hint to instructors and students: I would not recommend this suicidal pace, unless your students are very ambitious and/or very bright!)

The goal of the book is ambititous, and yet very simple. One of the biggest difficulties with voting theory and social choice is the "curse of integers or discreteness" - when we consider more than three alternatives, the number of alternative arrangements of voter preferences escalates quickly. This means that the main ideas in voting theory cannot usually be represented or analyzed by drawing a picture or using calculus, unlike most ideas in economics (eg the Edgeworth Box, demand/supply etc).

Saari avoids this problem by working with continuous spaces; he uses the geometry of the unit simplex (a familiar tool for most economics grad students) and the unit cube to analyze and explain just about all of the most important issues and results in social choice theory: cycling, manipulation, voting paradoxes, Arrow's theorem, Sen's theorem, the Gibbard-Satterthwaite theorem, and much, much more.

But the geometric approach is not just a cute pedagogic tool. On the contrary, the methods in this book allow researchers to state and prove new conjectures about voting methods using standard ideas from calculus, linear algebra, and basic high-school geometry; without these tools new results would be nearly impossible to even state, let alone prove.

The writing style is mostly informal, and many statements are not proved rigorously (they have only just recently appeared in the professional journal literature). Depending on your background this is either good or bad; but those with a graduate math background (like myself) can just go to the journals to find the proofs of statements if they so desire.

Probably the best part of the book is that there is a massive collection of problems at the end of each section - and many of the these problems are research questions in their own right. The other fun part of the book is that once you have learned to use Saari's geometric tools, you can create just about any crazy voting paradox you like in a couple of minutes, whereas this previously might have taken months or would constitute an entire research project. Therefore the book is very stimulating for advanced grad students and researchers in the field, as well as those encountering social choice theory for the first time.

Grad students - as a final inducement for reading this book, once you learn Saari's tools, you will be able to embarass about 99% of your professors and fellow students with your newly acquired skills. It is easy to find questions that are simply impossible to answer without using Saari's tools.

I would recommend the book to advanced graduate students in economics, mathematics and political science, and researchers in those fields.

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Mastering Fashion Buying and Merchandising Management (Palgrave Master)
Tim Jackson , and David Shaw
Manufacturer: Palgrave Macmillan
ProductGroup: Book
Binding: Paperback

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ASIN: 0333801652

Book Description

Developed and significantly expanded from a special issue of the Journal of European Public Policy, this volume draws on the insights from the recently emerging theoretically-informed literature on the EU's eastern enlargement and complements these studies with original articles that combine a theoretical approach with comparative analyses. The expert contributors focus on the broader theoretical debates and their implications for the enlargement of the EU, as well as placing the enlargement of the EU within the broader context of the expansion of international organizations and the study of institutions in international relations.

This volume is a key reference text presenting the 'state of the art' of theoretical approaches to the study of European enlargement.

Book Description

Provides the reader with an historical perspective on the development of materials used to toughen brittle plastics--like PVC and its copolymers--during the melt compounding process. In addition to a chronology of inventions and innovations, it features the Impact Modification Theory, its practical use (including choice of modifier, formulation and applications) and commercially available modifiers.

Plastics Additives and Modifiers Handbook

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Plastics Additives and Modifiers Handbook

Manufacturer: Van Nostrand Reinhold
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books
ASIN: 0442234503

Polymer Modifiers and Additives (Plastics Engineering)

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Dr Dick is the best.

Polymer Modifiers and Additives (Plastics Engineering)

Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

General & Reference | Chemistry | Science | Subjects | Books

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ASIN: 0824799496

Book Description

"Outlines the benefits of using additives-individually or in combination-to modify the properties and processability of pure polymers, and discusses easy-to-understand theory and practical applications for immediate economic and performance improvements."

Customer Reviews:

Dr Dick is the best........2001-03-02

This is an excellent and broad review of polymer additive san modifiers. It is very useful both for industry novices and for those branching out to new industry segments.

Impact modifiers: multiplying roles. (polyolefins and engineering resins functioning as both compatibilizer and toughener)(includes related article) (Additives ... Story): An article from: Plastics Technology

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Impact modifiers: multiplying roles. (polyolefins and engineering resins functioning as both compatibilizer and toughener)(includes related article) (Additives ... Story): An article from: Plastics Technology
Richard Monks
Manufacturer: Gardner Publications, Inc.
ProductGroup: Book
Binding: Digital

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Book Description

This digital document is an article from Plastics Technology, published by Gardner Publications, Inc. on July 1, 1992. The length of the article is 1419 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Impact modifiers: multiplying roles. (polyolefins and engineering resins functioning as both compatibilizer and toughener)(includes related article) (Additives '92: Formulations in Flux) (Cover Story)
Author: Richard Monks
Publication: Plastics Technology (Magazine/Journal)
Date: July 1, 1992
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Volume: v38 Issue: n7 Page: p61(3)

Article Type: Cover Story

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Izod Impact Strength of a Product Molded of Poly(Vinyl Chloride)/Impact Modifier Containing Voids (Void MOD).: An article from: Polymer Engineering and Science

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Izod Impact Strength of a Product Molded of Poly(Vinyl Chloride)/Impact Modifier Containing Voids (Void MOD).: An article from: Polymer Engineering and Science
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This digital document is an article from Polymer Engineering and Science, published by Society of Plastics Engineers, Inc. on March 1, 2001. The length of the article is 3743 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Izod Impact Strength of a Product Molded of Poly(Vinyl Chloride)/Impact Modifier Containing Voids (Void MOD).
Author: Akira Takaki
Publication: Polymer Engineering and Science (Refereed)
Date: March 1, 2001
Publisher: Society of Plastics Engineers, Inc.
Volume: 41 Issue: 3 Page: 575

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Polymer modifiers & additives.(seminar)(Brief Article): An article from: Plastics Engineering

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Polymer modifiers & additives.(seminar)(Brief Article): An article from: Plastics Engineering

Manufacturer: Society of Plastics Engineers, Inc.
ProductGroup: Book
Binding: Digital
ASIN: B0008EY6TY
Release Date: 2005-07-29

Book Description

This digital document is an article from Plastics Engineering, published by Society of Plastics Engineers, Inc. on March 1, 2002. The length of the article is 471 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Polymer modifiers & additives.(seminar)(Brief Article)
Publication: Plastics Engineering (Refereed)
Date: March 1, 2002
Publisher: Society of Plastics Engineers, Inc.
Volume: 58 Issue: 3 Page: SS17(1)

Article Type: Brief Article

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Enhancing Polymers Using Additive and Modifiers I: Conference Proceedings

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Enhancing Polymers Using Additive and Modifiers I: Conference Proceedings

Manufacturer: Rapra Technology
ProductGroup: Book
Binding: Paperback

Enhancing Polymers Using Additive and Modifiers II: Conference Proceedings

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Enhancing Polymers Using Additive and Modifiers II: Conference Proceedings

Manufacturer: Rapra Technology
ProductGroup: Book
Binding: Paperback

Book Description

In recent years, there has been an explosion of interest in the science of adhesion. Despite its multidisciplinary and undoubtedly industrial character, the wealth of phenomena to be found in the study of adhesion has drawn researchers from many seemingly disparate scientific disciplines. The intention of these books is to provide an updated view of the state of the art of adhesion science and to fill in the rather large gap in the compilation of knowledge related to adhesion science.

This set of two volumes describes adhesion science from three fundamental perspectives: mechanics, surfaces and chemistry. Volume 1 focuses attention on the contribution of mechanic principles and solutions to understanding the fabrication, design, analysis, and testing of adhesive bonds. It also offers a comprehensive overview of the current understanding of stresses, deformation, and fracture parameters associated with a range of adhesive bonds. Volume 2 dea

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Surfaces, Chemistry and Applications, Volume 2 : Adhesion Science and Engineering (Adhesion Science and Engineering)
Pocius
Manufacturer: NY
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Binding: Hardcover
ASIN: B000MUBFRK

Book Description

21st Century successor to _The Devil's Dictionary_

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