Excursions in Modern Mathematics, Books a la Carte Edition Plus MyLab Math -- Access Card Package (9th Edition)
9th Edition
ISBN: 9780134765839
Author: Peter 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
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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An election resulted in Candidate A winning, with Candidate B coming in a close second, and candidate C being a distant third.If in a head-to-head comparison a majority of people prefer B to A or C, which is the primary fairness criterion violated in this election?
Condorcet Criterion
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Majority Criterion
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An election resulted in Brown winning, with Kelly coming in a close second, and candidate Whitmore being a distant third. If in a head-to-head comparison a majority of people prefer Kelly to Brown or Whitmore, which is the primary fairness criterion violated in this election?
Condorcet Criterion
Independence of Irrelevant Alternatives (IIA) Criterion
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An election resulted in Brown winning, with Kelly coming in a close second, and Whitmore being a distant third. If Kelly had received a majority of first place votes, which is the primary fairness criterion violated in this election?
Independence of Irrelevant Alternatives (IIA) Criterion
Condorcet Criterion
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Majority Criterion
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Chapter 1 Solutions
Excursions in Modern Mathematics, Books a la Carte Edition Plus MyLab Math -- Access Card Package (9th Edition)
Ch. 1 - Figure 1-8 shows the preference ballots for an...Ch. 1 - Figure 1-9 shows the preference ballots for an...Ch. 1 - An election is held to choose the Chair of the...Ch. 1 - The student body at Eureka High School is having...Ch. 1 - An election is held using the printed-names format...Ch. 1 - Prob. 6ECh. 1 - Prob. 7ECh. 1 - Table 1-30 shows a conventional preference...Ch. 1 - The Demublican Party is holding its annual...Ch. 1 - The Epicurean Society is holding its annual...
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- The following statements are true except (a) The plurality method of voting satisfies the majority criterion. (b) The Borda count method of voting always violates the majority criterion. (c) The plurality-with-elimination method of voting satisfies the majority criterion. (d) The pairwise comparison method of voting satisfies the head-to-head criterionarrow_forwardIf Peter is preferred over Ned in a head-to-head comparison and Peter is preferred over MJ and Peter is preferred over May, then Ned should win the election. Does this satisfy the Condorcet Criterion? a. No, because it should be Peter. b. No, because it should be MJ. c. Yes, because it is an election. d. Yes, because it is a one-on-one comparison. It is sometimes called a “winner-take-all” method. a. Plurality Method b. Borda Count Method c. Pairwise Comparison d. Plurality with Eliminationarrow_forwardA group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) (ACB) (CAB) 10 4 5 Who wins the election using the Hare method? Does this violate the Condorcet criterion?arrow_forward
- Which fairness criterion is always satisfied by the plurality with elimination method? monotonicity criterion irrelevant alternatives criterion head-to-head criterion majority criterionarrow_forwardConsider the apportionment of 60 doctors for a physicians organization. The apportionment using Hamilton's method is shown in the table below. Does the Alabama paradox occur using Hamilton's method if the number of doctors is increased from 60 to 61? Clinic A B C D E Total Patients 656 536 515 549 602 2858 Standard quota 13.77 11.25 10.81 11.53 12.64 60.00 Lower quota 13 11 10 11 12 57 Hamilton's apportionment 14 11 11 11 13 60 Complete the table below with the new apportionment for clinics A, B, C, D, and E using a standard divisor rounded to two decimal places. Clinic A B C D E Total Patients 656 536 515 549 602 2858 Hamilton's apportionment ? ? ? ? ? 61arrow_forwardA group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) 4 (ACB) 8 (CAB) 6 Who wins the election using the Hare method? Answer Alice, Betty, or Connie. Does this violate the Condorcet criterion? Answer yes or no.arrow_forward
- Using the Plurality method of voting, what project should be implemented by the local advocacy group? G E W P 2. Using the Pairwise comparison method of voting, which of the following fairness in voting will NOT be violated? a. Majority criterion b. Condorcet criterion and Independence of irrelevant alternatives criterion c. Monotonicity criterion d. None of the above. 3. Suppose that 57 people who voted for water conservation (W) first and promoting local business (P) second changed their votes such that they all voted for promoting local business (P) first and water conservation (W) second. Which project will win using the Borda count method of voting? G E W Parrow_forwardAn exit poll of voters yielded the following information regarding voting patterns on propositions A, B, and C: 294 voters votes yes on A; 90 voted yes only on A, 346 voted yes on B, 166 voted yes only on B, 517 voted yes on A or B, 339 voted yes on C, no one voted yes on all three, and 72 voted no on all three. a) Sketch a venn diagram b) What percent of the voters voted no on A? c) What percent of the voters voted yes on more than one proposition?arrow_forwardPLEASE HELP Which fairness criteria, if any, were violated by using Plurality-with-elimination? LAST QUESTIONarrow_forward
- 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.arrow_forwardA. 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.arrow_forwardNumber 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?arrow_forward
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