Mathematics of Politics

ISBN-10: 1439819831
ISBN-13: 9781439819838
Edition: 2010
List price: $41.99 Buy it from $28.93
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Book details

List price: $41.99
Copyright year: 2010
Publisher: CRC Press LLC
Publication date: 12/9/2010
Binding: Hardcover
Pages: 477
Size: 6.50" wide x 9.25" long x 0.75" tall
Weight: 2.002
Language: English

George Washington University, Washington, District of Columbia, USA

Preface for the Reader
Preface for the Instructor
Voting
Introduction to Part I
Two Candidates
Scenario
Two-Candidate Methods
Supermajority and Status Quo
Weighted Voting and Other Methods
Criteria
May�s Theorem
Exercises and Problems
Social Choice Functions
Scenario
Ballots
Social Choice Functions
Alternatives to Plurality
Some Methods on the Edge
Exercises and Problems
Criteria for Social Choice
Scenario
Weakness and Strength
Some Familiar Criteria
Some New Criteria
Exercises and Problems
Which Methods Are Good?
Scenario
Methods and Criteria
Proofs and Counterexamples
Summarizing the Results
Exercises and Problems
Arrow�s Theorem
Scenario
The Condorcet Paradox
Statement of the Result
Decisiveness
Proving the Theorem
Exercises and Problems
Variations on the Theme
Scenario
Inputs and Outputs
Vote-for-One Ballots
Approval Ballots
Mixed Approval/Preference Ballots
Cumulative Voting
Condorcet Methods
Social Ranking Functions
Preference Ballots with Ties
Exercises and Problems
Notes on Part I
Apportionment
Introduction to Part II
Hamilton�s Method
Scenario
The Apportionment Problem
Some Basic Notions
A Sensible Approach
The Paradoxes
Exercises and Problems
Divisor Methods
Scenario
Jefferson�s Method
Critical Divisors
Assessing Jefferson�s Method
Other Divisor Methods
Rounding Functions
Exercises and Problems
Criteria and Impossibility
Scenario
Basic Criteria
Quota Rules and the Alabama Paradox
Population Monotonicity
Relative Population Montonicity
The New States Paradox
Impossibility
Exercises and Problems
The Method of Balinski and Young
Scenario
Tracking Critical Divisors
Satisfying the Quota Rule
Computing the Balinski-Young Apportionment
Exercises and Problems
Deciding among Divisor Methods
Scenario
Why Webster Is Best
Why Dean Is Best
Why Hill Is Best
Exercises and Problems
History of Apportionment in the United States
Scenario
The Fight for Representation
Summary
Exercises and Problems
Notes on Part II
Conflict
Introduction to Part III
Strategies and Outcomes
Scenario
Zero-Sum Games
The Naive and Prudent Strategies
Best Response and Saddle Points
Dominance
Exercises and Problems
Chance and Expectation
Scenario
Probability Theory
All Outcomes Are Not Crated Equal
Random Variables and Expected Value
Mixed Strategies and Their Payoffs
Independent Processes
Expected Payoffs for Mixed Strategies
Exercises and Problems
Solving Zero-Sum Games
Scenario
The Best Response
Prudent Mixed Strategies
An Application to Counterterrorism
The 2-by-2 Case
Exercises and Problems
Conflict and Cooperation
Scenario
Bimatrix Games
Guarantees, Saddle Points, and All That Jazz
Common Interests
Some Famous Games
Exercises and Problems
Nash Equilibria
Scenario
Mixed Strategies
The 2-by-2 Case
The Proof of Nash�s Theorem
Exercises and Problems
The Prisoner�s Dilemma
Scenario
Criteria and Impossibility
Omnipresence of the Prisoner�s Dilemma
Repeated Play
Irresolvability
Exercises and Problems
Notes on Part III
The Electoral College
Introduction to Part IV
Weighted Voting
Scenario
Weighted Voting Methods
Non-Weighted Voting Methods
Voting Power
Power of the States
Exercises and Problems
Whose Advantage?
Scenario
Violations of Criteria
People Power
Interpretation
Exercises and Problems
Notes on Part IV
Solutions to Odd-Numbered Exercises and Problems
Bibliography
Index

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