Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
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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If 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 Elimination
A voter who has a weight that is greater than or equal to the quota is called a dictator. In a weighted voting system, the dictator has all the power. A voter who is never a critical voter has no power and is referred to as a dummy. This term is not meant to be a comment on the voter’s intellectual powers; it just indicates that the voter has no ability to influence an election.
a. dictators : v1,v2 ; dummies : v2,v3
b. dictator : v1; dummies : v2,v3,v4,v5
c. dictator : v1; dummy : v2
d. The system is not valid.
Alex believes the honor roll students at his school have an unfair advantage in being assigned to the science class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the science class you requested?" The results are shown in the table below:
Help Alex determine if all students at his school have an equal opportunity to get into the science class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Chapter 1 Solutions
Excursions in Modern Mathematics (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
- In an election , it is possible that the winner of all pairwise comparisons with the other candidates loses the election. In this scenario, which fairness criterion is violated? O a. Condorcet Criterion O b. Majority Criterion О с. Independence of Irrelevant Alternatives Criterion O d. Monotonicity Criterionarrow_forwardA professional organization for lion tamers does an approval election for their president. The X below indicates approval. Percentage of Voters 15 3 16 28 31 7 Graves X X X Tuttle X X X Jones X X A) Which person wins the approval election? (Show vote totals) In any Approval election, what effect does a voter who approves of all the candidates have on the outcome of the election? B)arrow_forwardBorda method always satisfies the following fairness criteria based on Arrow's Impossibility Theorem: No answer provided a. Majority criterion and monotonicity criterion b. Majority criterion and heat-to-head criterion c. Head-to-head criterion and irrelevant alternatives criterion d. none of the abovearrow_forward
- 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 Majority Criterion No fairness criteria are violated Monotonicity Criterionarrow_forwardReports have found that many U.S. adults would rather live in a different type of community than where they are living. A national survey of 2260 adults asked: "Where do you live now?", and "What do you consider to be the ideal community?" Response options were City (C), Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows: Question 1: Where do you live now? S T R C R S S C S S T R S S T C C R T C S S C C S C T R R C T S S S S C S C S T T C S T C T C T C R C C R S C C R T C R T R S R T R T C S T T T C C S C S C T C S S T S C C R T T T T C C R T S C C R S Question 2: What do you consider to be the ideal community? S R C T T C T T C T S S S T T C T T C R S T C C S C T R C S T S T T R C T T R S C R T S R R R S C R T C S T T T T S T T S T R R T C C S R R R C T R S R T T T S C T S C T S S R T T C R T R T R R C R T EXCEL…arrow_forward
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