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Basic Geometry of Voting Paperback – October 4, 2013

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Editorial Reviews

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My review of Geometry of Voting was enthusiastic. A last comment: If you have a copy of it, get a copy of Basic Geometry of Voting also; if you haven't, get both. -- Maurice Salles, Mathematical Reviews, issue 98d
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Product Details

  • Paperback: 300 pages
  • Publisher: Springer; 1995 edition (October 4, 2013)
  • Language: English
  • ISBN-10: 3540600647
  • ISBN-13: 978-3540600640
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #2,691,814 in Books (See Top 100 in Books)

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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.
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Format: Paperback
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.
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