ch01 - Excursions in Modern Mathematics Sixth Edition Peter...

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1 Excursions in Modern Mathematics Sixth Edition Peter Tannenbaum
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2 Chapter 1 The Mathematics of Voting The Paradoxes of Democracy
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3 The Mathematics of Voting Outline/learning Objectives Construct and interpret a preference schedule for an election involving preference ballots. Implement the plurality, Borda count, plurality-with- elimination, and pairwise comparisons vote counting methods. Rank candidates using recursive and extended methods. Identify fairness criteria as they pertain to voting methods. Understand the significance of Arrows’ impossibility theorem.
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4 The Mathematics of Voting 1.1 Preference Ballots and Preference Schedules
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5 The Mathematics of Voting Preference ballots Preference ballots A ballot in which the voters are asked to rank the candidates in order of preference. Linear ballot Linear ballot A ballot in which ties are not allowed.
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6 The Mathematics of Voting
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7 The Mathematics of Voting schedule: schedule: A preference A preference
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8 The Mathematics of Voting Important Facts The first is that a voter’s preference are transitive transitive , i.e., that a voter who prefers candidate A over candidate B and prefers candidate B over candidate C automatically prefers candidate A over C. Secondly, that the relative preferences of a voter are not affected by the elimination of one or more of the candidates.
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9 The Mathematics of Voting Relative Preferences of a Voter
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10 The Mathematics of Voting Relative Preferences by elimination of one or more candidates
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11 The Mathematics of Voting 1.2 The Plurality Method
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12 The Mathematics of Voting Plurality method Plurality method Election of 1 st place votes Plurality candidate Plurality candidate The Candidate with the most 1 st place votes
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13 The Mathematics of Voting Majority rule Majority rule The candidate with a more than half the votes should be the winner. Majority candidate Majority candidate The candidate with the majority of 1 st place votes .
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14 The Mathematics of Voting The Majority Criterion The Majority Criterion If candidate X has a majority of the 1 st place votes, then candidate X should be the winner of the election.
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