A mathematical look at politics. (2010)

• Record Type: Book
• Further Information: Note: E. Arthur Robinson, Daniel Ullman.
• Other Names: Robinson, E. Arthur, 1955-; Ullman, Daniel
• Contents: Preface, for the Student; Preface, for the Instructor ; Voting; 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 ; 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 monotonicity; 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 ; 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 created equal; Random variables and expected value; Mixed strategies and their payouts; Independent processes; Expected payouts for mixed strategies; Exercises and Problems; Solving Zero-Sum Games; Scenario; The best response ; Prudent mixed strategies; An application to counterterrorism; The -by- 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 -by- 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; 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 ;
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2010
• Extent: 1 online resource, illustrations
• Subjects: 320.01513; Political science -- Mathematics
• Languages: English
• ISBNs: 9781439891179; 1439891176
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.