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A MATHEMATICAL LOOK AT POLITICS

Arthur Robinson Jr. E.

Oprawa:
TWARDA

Wydawca:
Taylor and Francis

Data premiery:
2010-12-17

ISBN:
9781439819838

230,95 PLN
Wysyłamy w 21 dni

Opis produktu

P>What Ralph Naders spoiler role in the 2000 presidential election tells us about the American political system. Why Montana went to court to switch the 1990 apportionment to Deans method. How the US tried to use game theory to win the Cold War and why it didnt work. When students realize that mathematical thinking can address these sorts of pressing concerns of the political world it naturally sparks their interest in the underlying mathematics. /P>P>STRONG>A Mathematical Look at Politics /STRONG>is designed as an alternative to the usual mathematics texts for students in quantitative reasoning courses. It applies the power of mathematical thinking to problems in politics and public policy. Concepts are precisely defined. Hypotheses are laid out. Propositions lemmas theorems and corollaries are stated and proved. Counterexamples are offered to refute conjectures. Students are expected not only to make computations but also to state results prove them and draw conclusions about specific examples./P>P>Tying the liberal arts classroom to realworld mathematical applications this text is more deeply engaging than a traditional general education book that surveys the mathematical landscape. It aims to instill a fondness for mathematics in a population not always convinced that mathematics is relevant to them.P>STRONG>Preface for the StudentPreface for the Instructor/STRONG>/P>P>STRONG>U>Voting /U>/STRONG>STRONG>Two Candidates /STRONG>Scenario Twocandidate methods Supermajority and status quo Weighted voting and other methodsCriteriaMays Theorem Exercises and problems STRONG>Social Choice Functions /STRONG>Scenario BallotsSocial choice functions Alternatives to plurality Some methods on the edge Exercises and problems STRONG>Criteria for Social Choice /STRONG>Scenario Weakness and strength Some familiar criteriaSome new criteriaExercises and problems STRONG>Which Methods are Good? /STRONG>Scenario Methods and criteriaProofs and counterexamplesSummarizing the results Exercises and problems STRONG>Arrows Theorem /STRONG>Scenario The Condorcet paradox Statement of the result Decisiveness Proving the theorem Exercises and problems STRONG>Variations on the Theme /STRONG>Scenario Inputs and outputs Voteforone ballots Approval ballots Mixed approval/preference ballots Cumulative voting . Condorcet methods Social ranking functions Preference ballots with ties Exercises and problems STRONG>Notes on Part I /STRONG>/P>P>U>STRONG>Apportionment /STRONG>/U>STRONG>Hamiltons Method /STRONG>Scenario The apportionment problemSome basic notions A sensible approach The paradoxesExercises and problems STRONG>Divisor Methods /STRONG>Scenario Jeffersons method Critical divisors Assessing Jeffersons methodOther divisor methodsRounding functionsExercises and problems STRONG>Criteria and Impossibility /STRONG>Scenario Basic criteria Quota rules and the Alabama paradox Population monotonicityRelative population monotonicity The new states paradox Impossibility Exercises an

Data Publikacji: 2010-12-17
Wymiary: 234 mm 156 mm 839.15 gr

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