USING AND UNDERSTANDING MATHEMATICS W/
7th Edition
ISBN: 9780135239919
Author: BENNETT AND BR
Publisher: PEARSON
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Textbook Question
Chapter 12.B, Problem 18E
Sequential Runoff and Criterion 2. Devise a preference schedule with three candidates and three rankings such that the sequential runoff method violates Fairness Criterion 2. Explain your work.
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Compare and contrast the Borda count method and the purality-with-elimination method. Identify at least one similarity and one difference. Use a specific example of voting preferences to illustrate your point.
1. Who is the winner using the Borda Count? Justify your answer.
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3. Who is the winner using pairwise comparison method? Justify your answer.
Number of voters
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2ND Choice
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10
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Chapter 12 Solutions
USING AND UNDERSTANDING MATHEMATICS W/
Ch. 12.A - Prob. 1QQCh. 12.A - Prob. 2QQCh. 12.A - Prob. 3QQCh. 12.A - Prob. 4QQCh. 12.A - Prob. 5QQCh. 12.A - Prob. 6QQCh. 12.A - Prob. 7QQCh. 12.A - Prob. 8QQCh. 12.A - 9. Study Table 12.5. Which candidate received the...Ch. 12.A - 10. What is the primary lesson of the preference...
Ch. 12.A - 1. What is majority rule? When can it definitively...Ch. 12.A - Prob. 2ECh. 12.A - What is a filibuster? What percentage of the vote...Ch. 12.A - Prob. 4ECh. 12.A - Prob. 5ECh. 12.A - Prob. 6ECh. 12.A - Prob. 7ECh. 12.A - Prob. 8ECh. 12.A - Prob. 9ECh. 12.A - Prob. 10ECh. 12.A - 11. Herman won a plurality of the vote, but Hanna...Ch. 12.A - Fred beat Fran using the point system (Borda...Ch. 12.A - 13. Candidate Reagan won the popular vote for the...Ch. 12.A - Prob. 14ECh. 12.A - Prob. 15ECh. 12.A - Prob. 16ECh. 12.A - Prob. 17ECh. 12.A - Prob. 18ECh. 12.A - Prob. 19ECh. 12.A - Presidential Elections. The following tables give...Ch. 12.A - Prob. 21ECh. 12.A - Prob. 22ECh. 12.A - Prob. 23ECh. 12.A - Presidential Elections. The following tables give...Ch. 12.A - 23. Super Majorities.
a. Of the 100 senators in...Ch. 12.A - 24. Super Majorities.
a. According to the bylaws...Ch. 12.A - Prob. 27ECh. 12.A - Prob. 28ECh. 12.A - Prob. 29ECh. 12.A - Prob. 30ECh. 12.A - Prob. 31ECh. 12.A - Prob. 32ECh. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - 31—34. Interpreting Preference Schedules. Answer...Ch. 12.A - Prob. 36ECh. 12.A - Prob. 37ECh. 12.A - Prob. 38ECh. 12.A - Prob. 39ECh. 12.A - Prob. 40ECh. 12.A - Prob. 41ECh. 12.A - How Close Was 2016? Consider Table 12.3 which...Ch. 12.A - Prob. 43ECh. 12.A - Prob. 44ECh. 12.A - Prob. 45ECh. 12.A - Prob. 46ECh. 12.A - Condorcet Winner. If a candidate wins all...Ch. 12.A - 45. Condorcet Paradox. Consider the following...Ch. 12.A - 46. Pairwise Comparisons Question.
a. How many...Ch. 12.A - Prob. 50ECh. 12.A - Prob. 51ECh. 12.A - Prob. 52ECh. 12.A - Prob. 53ECh. 12.A - Prob. 54ECh. 12.A - Sports Polls. Most men’s and women’s major college...Ch. 12.A - Elections Around the World. Many countries have...Ch. 12.B - l. How many of the four fairness criteria (see p....Ch. 12.B - Prob. 2QQCh. 12.B - Prob. 3QQCh. 12.B - Prob. 4QQCh. 12.B -
5. Suppose that Berman is declared the winner of...Ch. 12.B - 6. Suppose that Freedman is declared the winner of...Ch. 12.B - 7. Notice that if Goldsmith dropped out, Freedman...Ch. 12.B - Prob. 8QQCh. 12.B - Which of the following is not an advantage of...Ch. 12.B - Prob. 10QQCh. 12.B - Briefly summarize each of the four fairness...Ch. 12.B - Prob. 2ECh. 12.B - What is approval voting? How is it different from...Ch. 12.B - Prob. 4ECh. 12.B - Prob. 5ECh. 12.B - Prob. 6ECh. 12.B - Prob. 7ECh. 12.B - Prob. 8ECh. 12.B - Plurality and Criterion 1. Explain in words why...Ch. 12.B - 10. Plurality and Criterion 2. Consider the...Ch. 12.B - 11. Plurality and Criterion 2. Devise a preference...Ch. 12.B - Prob. 12ECh. 12.B - Plurality and Criterion 4. Suppose the plurality...Ch. 12.B - Prob. 14ECh. 12.B - Runoff Methods and Criterion 1. Explain in words...Ch. 12.B - Prob. 16ECh. 12.B - Prob. 17ECh. 12.B - Sequential Runoff and Criterion 2. Devise a...Ch. 12.B - Prob. 19ECh. 12.B - Prob. 20ECh. 12.B - Prob. 21ECh. 12.B - Prob. 22ECh. 12.B - Point System and Criterion 1. Devise your own...Ch. 12.B - 24. Point System and Criterion 2. Suppose the...Ch. 12.B - 25. Point System and Criterion 2. Devise a...Ch. 12.B - Prob. 26ECh. 12.B - Prob. 27ECh. 12.B - Prob. 28ECh. 12.B - Prob. 29ECh. 12.B - Prob. 30ECh. 12.B - Prob. 31ECh. 12.B - Pairwise Comparisons and Criterion 4. Suppose the...Ch. 12.B - Prob. 33ECh. 12.B - Approval Voting. Suppose that Candidates A and B...Ch. 12.B - Prob. 35ECh. 12.B - Power Voting. Imagine that a small company has...Ch. 12.B - 37-41: Electoral Power. Use the table below to...Ch. 12.B - 37-41: Electoral Power. Use the table below to...Ch. 12.B - Prob. 39ECh. 12.B - Prob. 40ECh. 12.B - Prob. 41ECh. 12.B - Prob. 42ECh. 12.B - Prob. 43ECh. 12.B - Prob. 44ECh. 12.B - Prob. 45ECh. 12.B - Prob. 46ECh. 12.B - Prob. 47ECh. 12.B - Prob. 48ECh. 12.B - Prob. 49ECh. 12.B - Prob. 50ECh. 12.B - Prob. 51ECh. 12.B - 52. Swing Votes. Suppose that the following...Ch. 12.B - Prob. 53ECh. 12.B - Other Fairness Criteria. The fairness criteria...Ch. 12.B - Prob. 55ECh. 12.B - Power Voting and Coalitions. Use the Web...Ch. 12.B - General Voting Power. Find the news report about...Ch. 12.B - Prob. 58ECh. 12.C - Prob. 1QQCh. 12.C - Prob. 2QQCh. 12.C - Prob. 3QQCh. 12.C - 4. Suppose that, in 2030, the census shows that...Ch. 12.C - 5. Consider a school district with 50 schools,...Ch. 12.C - 6. Consider the school district described in...Ch. 12.C - Prob. 7QQCh. 12.C - Prob. 8QQCh. 12.C - Prob. 9QQCh. 12.C - Prob. 10QQCh. 12.C - Prob. 1ECh. 12.C - Prob. 2ECh. 12.C - Prob. 3ECh. 12.C - What is the Alabama paradox? What other paradoxes...Ch. 12.C - Prob. 5ECh. 12.C - What is the quota criterion? Why are violations of...Ch. 12.C - 7. Briefly describe how Webster’s method and the...Ch. 12.C - 8. Explain why Webster’s method and the...Ch. 12.C - is the president of a large company with 12...Ch. 12.C - 10. Charlene is the head judge in a figure skating...Ch. 12.C - Prob. 11ECh. 12.C - Prob. 12ECh. 12.C - Prob. 13ECh. 12.C - Prob. 14ECh. 12.C - Prob. 15ECh. 12.C - Prob. 16ECh. 12.C - Prob. 17ECh. 12.C - 15-18: State Representation. The following table...Ch. 12.C - 19. Standard Quotas in Business. A large company...Ch. 12.C - 20. Standard Quota in Education. Capital...Ch. 12.C - Prob. 21ECh. 12.C - Prob. 22ECh. 12.C - Prob. 23ECh. 12.C - Prob. 24ECh. 12.C - Prob. 25ECh. 12.C - Prob. 26ECh. 12.C - Prob. 27ECh. 12.C - Prob. 28ECh. 12.C - Prob. 29ECh. 12.C - Prob. 30ECh. 12.C - 29-32: Jefferson's Method. Apply Jefferson's...Ch. 12.C - Jefferson's Method. Apply Jefferson's method to...Ch. 12.C - 33. Webster’s Method. Use Webster’s method to...Ch. 12.C - 34. Webster’s Method. Use Webster’s method to...Ch. 12.C - Prob. 35ECh. 12.C - Prob. 36ECh. 12.C - Prob. 37ECh. 12.C - Prob. 38ECh. 12.C - Comparing Methods. Assume 100 delegates are to be...Ch. 12.C - Prob. 40ECh. 12.C - Prob. 41ECh. 12.C - 39-42: Comparing Methods. Assume 100 delegates are...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - 43-46: Non-House Apportionments. The following...Ch. 12.C - Prob. 46ECh. 12.C - Prob. 47ECh. 12.C - Prob. 48ECh. 12.C - Prob. 49ECh. 12.D - Prob. 1QQCh. 12.D - Prob. 2QQCh. 12.D - 3. If we compare results in presidential elections...Ch. 12.D - 4. In 2010, Republicans in North Carolina received...Ch. 12.D - Prob. 5QQCh. 12.D - Prob. 6QQCh. 12.D - Prob. 7QQCh. 12.D - Prob. 8QQCh. 12.D - Prob. 9QQCh. 12.D - Prob. 10QQCh. 12.D - What is redistricting, and when must it be done?Ch. 12.D - 2. How has the competitiveness of elections for...Ch. 12.D - 3. What is gerrymandering? Where does this term...Ch. 12.D - 4. Briefly describe how the drawing of boundaries...Ch. 12.D - What requirements must be met in drawing district...Ch. 12.D - Briefly describe two ideas for reforming the...Ch. 12.D - In the last election in my home state, 48% of the...Ch. 12.D - Prob. 8ECh. 12.D - Polls show that half voters in our state plan to...Ch. 12.D - Prob. 10ECh. 12.D - Prob. 11ECh. 12.D - Prob. 12ECh. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - Prob. 14ECh. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - 13-17: Redistricting and House Elections. The 2010...Ch. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D -
18-23: Average and Extreme Districts. Consider...Ch. 12.D - Prob. 19ECh. 12.D - Prob. 20ECh. 12.D - 18—23: Average and Extreme Districts. Consider the...Ch. 12.D - Average and Extreme Districts. Consider the...Ch. 12.D - Prob. 23ECh. 12.D - Prob. 24ECh. 12.D - Prob. 25ECh. 12.D - Prob. 26ECh. 12.D - Prob. 27ECh. 12.D - Prob. 28ECh. 12.D - 28—29: Drawing Districts Set III. Refer to Figure...Ch. 12.D - 30—32: Drawing Districts Set IV. Refer to Figure...Ch. 12.D - 30—32: Drawing Districts Set IV. Refer to Figure...Ch. 12.D - Prob. 32ECh. 12.D - Prob. 33ECh. 12.D - Prob. 34ECh. 12.D - Prob. 35ECh. 12.D - Prob. 36ECh. 12.D - Prob. 37ECh. 12.D - Prob. 38ECh. 12.D - Prob. 39ECh. 12.D - Prob. 40ECh. 12.D - Prob. 41ECh. 12.D - 42. Redistricting Procedures. Choose a state that...Ch. 12.D - 43. Reform Efforts. Investigate the current status...Ch. 12.D - 44. Mathematical Algorithms for Reform. Search for...Ch. 12.D - Prob. 45E
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- Apportionmentarrow_forwardA campus club has money left over in its budget and must spend it beforethe school year ends. The members arrive at five different possibilities, and each memberranks them in order of preference. The results are shown in the table below. 1. Using the Plurality method, how should they spend the money? 2. Use Plurality with elimination. to know how the money should be spent? 3. Using Pairwise Comparison, how should they spend the money? 4. Using the Borda count method of voting, how should the money be spent?5. In your opinion, which of the previous three methods seems most appropriate in thissituation? Why?arrow_forwardIn a weighted voting system with three players the winning coalitions are {P1, P2} and {P1, P2, P3}. List the sequential coalitions and identify the pivotal player in each sequential coalition. Then, find the Shapley-Shubik power distribution of the weighted voting system. Im pretty sure these are the Coalitions: P1, P2, P3 P1, P3, P2 P2, P1, P3 P2, P3, P1 P3,P1, P2 P3, P2, P1 My question: How do we find the pivotal players when we have not assigned values to each player? please show me that process in detail and then how to do the Shapley-Shubik power distribution. Thank youarrow_forward
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