EXCURSIONS IN MODERN MATH- MYMATHLAB
EXCURSIONS IN MODERN MATH- MYMATHLAB
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ISBN: 9780135902868
Author: Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 1, Problem 66E

The Pareto criterion. The following fairness criterion was proposed by Italian economist Vilfredo Pareto ( 1848 1923 ) ; If every voter prefers candidate X to candidate Y , then X should be ranked above Y .

a. Explain why the Borda count method satisfies the Pareto criterion.

b. Explain why the pair wise-comparisons method satisfies the Pareto criterion.

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Chapter 1 Solutions

EXCURSIONS IN MODERN MATH- MYMATHLAB

Ch. 1 - Table 1-31 shows the preference schedule for an...Ch. 1 - Table 1-32 shows the preference schedule for an...Ch. 1 - Table 1-33 shows the preference schedule for an...Ch. 1 - Table 1-34 shows the preference schedule for an...Ch. 1 - Table 1-35 shows the preference schedule for an...Ch. 1 - Table1-36 shows the preference schedule for an...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-25 see Exercise 3 shows the preference...Ch. 1 - Table 1-26 see Exercise 4 shows the preference...Ch. 1 - Table 1-31see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 Number of voters 6 6 5 4 3 3 1st A B B...Ch. 1 - Table 1-35 Percent of voters 24 23 19 14 11 9 1st...Ch. 1 - Table 1-36 Percent of voters 25 21 15 12 10 9 8...Ch. 1 - The Heisman Award. Table 1-37 shows the results...Ch. 1 - The 2014 AL Cy Young Award. Table 1-38 shows the...Ch. 1 - An election was held using the conventional Borda...Ch. 1 - Imagine that in the voting for the American League...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 see Exercise 12 shows the preference...Ch. 1 - Table1-33 Number of voters 6 5 4 2 2 2 2 1st C A B...Ch. 1 - Table 1-34 See Exercise 14 shows the preference...Ch. 1 - Table1-39_ shows the preference schedule for an...Ch. 1 - Table1-40_ shows the preference schedule for an...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Top-Two Instant-Runoff Voting. Exercises 39 and 40...Ch. 1 - Table 1-31 see Exercise 11 shows the preference...Ch. 1 - Table 1-32 See Exercise 12 shows the preference...Ch. 1 - Table 1-33 see Exercise 13 shows the preference...Ch. 1 - Table 1-34 see Exercise 14 shows the preference...Ch. 1 - Table 1-35 see Exercise 15 shows the preference...Ch. 1 - Table 1-36 see Exercise 16 shows the preference...Ch. 1 - Table 1-39 see Exercise 35 shows the preference...Ch. 1 - Table1-40 see Exercise36 shows the preference...Ch. 1 - An election with five candidates A, B. C, D, and E...Ch. 1 - An election with six candidates A, B, C, D, E, and...Ch. 1 - Use Table 1-41 to illustrate why the Borda count...Ch. 1 - Use Table 1-32 to illustrate why the...Ch. 1 - Use Table 1-42 to illustrate why the plurality...Ch. 1 - Use the Math Club election Example 1.10 to...Ch. 1 - Use Table 1-43 to illustrate why the...Ch. 1 - Explain why the method of pair wise comparisons...Ch. 1 - Prob. 57ECh. 1 - Explain why the plurality method satisfies the...Ch. 1 - Explain why the Borda count method satisfies the...Ch. 1 - Explain why the method of pairwise comparisons...Ch. 1 - Two-candidate elections. Explain why when there...Ch. 1 - Alternative version of the Borda count. The...Ch. 1 - Reverse Borda count. Another commonly used...Ch. 1 - The average ranking. The average ranking of a...Ch. 1 - The 2006 Associated Press college football poll....Ch. 1 - The Pareto criterion. The following fairness...Ch. 1 - The 2003-2004 NBA Rookie of the Year vote. Each...Ch. 1 - Top-two IRV is a variation of the...Ch. 1 - The Coombs method. This method is just like the...Ch. 1 - Bucklin voting. This method was used in the early...Ch. 1 - The 2016 NBA MVP vote. The National Basketball...Ch. 1 - The Condorcet loser criterion. If there is a...Ch. 1 - Consider the following fairness criterion: If a...Ch. 1 - Suppose that the following was proposed as a...Ch. 1 - Consider a modified Borda count where a...
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  • In an election with three candidates, A, B, and C, the voters have the following preferences: 12% approve of A only. 19% approve of A (first choice) but also approve of B. 17% approve of B (first choice) but also approve of A. 25% approve of C (first choice) but also approve of A. 27% approve of C (first choice) but also approve of B. a. Which candidate wins an approval vote? b. Fairness Criterion 1 states, “If a candidate receives a majority of the first-place votes, that candidate should be the winner.” Is this criterion satisfied in this election? Explain.
    A. How many voters are there?B. How many voters have ranked the candidates in the order C, B, A, D?C. What is the minimum number of voters needed to form a majority?D. Who is the winner using the Plurality Voting method?E. Find the points each candidate received using the basic Borda Count method.A = ____ points; B = ____ points; C = ____ points; D = ____ points.F. Who is the winner using the Hare system?G. Find the points each candidate received using the Pairwise Comparisonmethod.A = ____ points; B = ____ points; C = ____ points; D = ____ points.
    Number of voters 15 14 9 12 28 1st choice D A D C B 2nd choice B C A D D 3rd choice C D B B C 4th choice A B C A A Based on the sample of votes recorded:Who is the winner of the election using the Plurality method?Winner is Is there a Condorcet winner of the election? Enter None if there is no Condorcet winner.Winner is Was the head-to-head fairness criterion violated?
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