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