Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 1, Problem 58E
Explain why the plurality method satisfies the monotonicity criterion.
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Which fairness criterion is always satisfied by the
plurality with elimination method?
irrelevant alternatives criterion
majority criterion
head-to-head criterion
monotonicity criterion
Which fairness criterion is always satisfied by the plurality with elimination method?
monotonicity criterion
irrelevant alternatives criterion
head-to-head criterion
majority criterion
If a non-winning choice is removed from the ballot, this criterion states that the winner of the election should not change.
Monotonicity Criterion
Independence of Irrelevant Alternatives (IIA) Criterion
Majority Criterion
Condorcet Criterion
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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- Solve the problem. Which fairness criterion is always satisfied by the plurality with elimination method? O monotonicity criterion O majority criterion O irrelevant alternatives criterion O head-to-head criterionarrow_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_forwardWhat is the maximum number of points that a candidate can earn in an election using the Borda count method if there are four candidates and 20 voters?arrow_forward
- What is also the rejection criteria?arrow_forwardB) Are males or females do a better job of detecting cheating? Justify your answer using conditions needed to justify your answer .arrow_forwardPLEASE HELP Which fairness criteria, if any, were violated by using Plurality-with-elimination? LAST QUESTIONarrow_forward
- wat is the intermdiate demond of the agricultural,manufacutring,and energy sectorarrow_forwardOut of Plurality, Borda countSequential Pairwise voting and the Hare System, which one satisfies the Pareto Condition but is not monotone ? Explainarrow_forwardCounty school buses are inspected every month for “defects.” In a recent monthly inspection, 27 worn or tornseats were found, 22 buses had dirty floors, there were14 cases of exterior scratches and chipped paint, therewere 8 cracked or broken windows, the engines on 4buses had trouble starting or were not running smoothly,and 2 buses had faulty brakes. Develop a Pareto chart forthe bus inspections and indicate the most significantquality-problem categories. What does this tell you aboutthe limitations of applying Pareto chart analysis. Howmight these limitations be overcome in Pareto chartanalysis?arrow_forward
- What is the maximum number of points that a candidate can earn in an election using the pairwise comparison method if there are nine candidates?arrow_forwardPlease solve fast Use the following preference schedule to show that the Plurality method violates the Condorcet criterion.arrow_forwardExplain the difference between the three types of mergers. Which types of mergers are department of justic most likely to oppose? Why?arrow_forward
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