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Mathematics of Voting and Elections: a Hands-on Approach Second Edition [Pehme köide]

  • Formaat: Paperback / softback, 247 pages, kõrgus x laius: 254x178 mm, kaal: 440 g
  • Sari: Mathematical World
  • Ilmumisaeg: 30-Nov-2018
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470442876
  • ISBN-13: 9781470442873
Teised raamatud teemal:
  • Formaat: Paperback / softback, 247 pages, kõrgus x laius: 254x178 mm, kaal: 440 g
  • Sari: Mathematical World
  • Ilmumisaeg: 30-Nov-2018
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470442876
  • ISBN-13: 9781470442873
Teised raamatud teemal:
The Mathematics of Voting and Elections: A Hands-On Approach, Second Edition, is an inquiry-based approach to the mathematics of politics and social choice. The aim of the book is to give readers who might not normally choose to engage with mathematics recreationally the chance to discover some interesting mathematical ideas from within a familiar context, and to see the applicability of mathematics to real-world situations. Through this process, readers should improve their critical thinking and problem solving skills, as well as broaden their views of what mathematics really is and how it can be used in unexpected ways. The book was written specifically for non-mathematical audiences and requires virtually no mathematical prerequisites beyond basic arithmetic. At the same time, the questions included are designed to challenge both mathematical and non-mathematical audiences alike. More than giving the right answers, this book asks the right questions.

The book is fun to read, with examples that are not just thought-provoking, but also entertaining. It is written in a style that is casual without being condescending. But the discovery-based approach of the book also forces readers to play an active role in their learning, which should lead to a sense of ownership of the main ideas in the book. And while the book provides answers to some of the important questions in the field of mathematical voting theory, it also leads readers to discover new questions and ways to approach them.

In addition to make small improvements in all the chapters, this second edition contains several new chapters. Of particular interest might be Chapter 12 which covers a host of topics related to gerrymandering.
Preface ix
Acknowledgments xiii
Chapter 1 What's So Good About Majority Rule?
1(14)
The Mayor of Stickeyville
1(2)
Anonymity, Neutrality, and Monotonicity
3(2)
Majority Rule and May's Theorem
5(1)
Quota Systems
6(2)
Back to May's Theorem
8(2)
Questions for Further Study
10(2)
Answers to Starred Questions
12(3)
Chapter 2 Le Pen, Nader, and Other Inconveniences
15(18)
The Plurality Method
17(1)
The Borda Count
18(2)
Preference Orders
20(2)
Back to Borda
22(1)
May's Theorem Revisited
23(2)
Questions for Further Study
25(5)
Answers to Starred Questions
30(3)
Chapter 3 Back into the Ring
33(20)
Condorcet Winners and Losers
35(3)
Sequential Pairwise Voting
38(4)
Instant Runoff
42(3)
Putting It All Together
45(1)
Questions for Further Study
46(3)
Answers to Starred Questions
49(4)
Chapter 4 Trouble in Democracy
53(18)
Independence of Irrelevant Alternatives
54(4)
Arrow's Theorem
58(5)
Pareto's Unanimity Condition
63(2)
Concluding Remarks
65(1)
Questions for Further Study
65(3)
Answers to Starred Questions
68(3)
Chapter 5 Explaining the Impossible
71(20)
Proving Arrow's Theorem
72(7)
Potential Solutions
79(6)
Concluding Remarks
85(1)
Questions for Further Study
86(2)
Answers to Starred Questions
88(3)
Chapter 6 Gaming the System
91(14)
Strategic Voting
92(1)
The Gibbard-Satterthwaite Theorem
93(2)
Proving the Gibbard-Satterthwaite Theorem
95(6)
Concluding Remarks
101(1)
Questions for Further Study
102(1)
Answers to Starred Questions
103(2)
Chapter 7 One Person, One Vote?
105(16)
Weighted Voting Systems
106(3)
Dictators, Dummies, and Veto Power
109(1)
Swap Robustness
110(3)
Trade Robustness
113(2)
Questions for Further Study
115(3)
Answers to Starred Questions
118(3)
Chapter 8 Calculating Corruption
121(22)
The Banzhaf Power Index
122(3)
The Shapley-Shubik Power Index
125(3)
Banzhaf Power in Psykozia
128(2)
A Splash of Combinatorics
130(3)
Shapley-Shubik Power in Psykozia
133(2)
Questions for Further Study
135(3)
Answers to Starred Questions
138(5)
Chapter 9 The Ultimate College Experience
143(20)
The Electoral College
144(2)
The Winner-Take-All Rule
146(2)
Some History
148(1)
Power in the Electoral College
149(4)
Swing Votes and Perverse Outcomes
153(4)
Alternatives to the Electoral College
157(1)
Questions for Further Study
158(4)
Answers to Starred Questions
162(1)
Chapter 10 Trouble in Direct Democracy
163(22)
Even More Trouble
165(1)
The Separability Problem
166(2)
Binary Preference Matrices
168(1)
Testing for Separability
169(4)
Some Potential Solutions
173(6)
Questions for Further Study
179(3)
Answers to Starred Questions
182(3)
Chapter 11 Proportional (Mis)representation
185(22)
The U.S. House of Representatives
186(1)
Hamilton's Apportionment Method
187(3)
Jefferson's Apportionment Method
190(5)
Webster's Apportionment Method
195(1)
Three Apportionment Paradoxes
196(2)
Hill's Apportionment Method
198(2)
Another Impossibility Theorem
200(1)
Concluding Remarks
201(1)
Questions for Further Study
202(3)
Answers to Starred Questions
205(2)
Chapter 12 Choosing Your Voters
207(22)
Gerrymandering
209(5)
Rules for Redistricting
214(1)
Geometry and Compactness
215(3)
Partisan Symmetry
218(3)
The Efficiency Gap
221(2)
Concluding Remarks
223(1)
Questions for Further Study
224(3)
Answers to Starred Questions
227(2)
Bibliography 229(4)
Index 233
Jonathan K. Hodge, Grand Valley State University, Allendale, MI.

Richard E. Klima, Appalachian State University, Boone, NC.