To determine There are five parts to be determined in this question and these are: (a) To find apportionment using Hamilton’s method. (b) To find apportionment using Jefferson’s method. (c) To find apportionment using Webster’s method. (d) To find apportionment using Hill-Huntington’s method. (e) Compare results of various methods Explanation Given: Total 25 managers are to be apportioned. And sales of stores Boulder (A), Denver (B), Broomfield (C) and Collins (D) are 2.5, 7.6, 3.9 and 5.5 respectively. Formula Used: Standard divisor = total sales number of managers Standard quota = store sales standard divisor Calculations: Number of delegates to be apportioned = 25 Total number of members = 2.5 + 7.6 + 3.9 + 5.5 = 19.5 Calculate standard divisor Standard divisor = 19 .5 25 = 0.78 Calculate Standard quota for each store Standard quota = store sales 0.78 (These calculations are shown in the third row of the table below) Give each store the number of managers found by rounding its standard quota down. This number is the state’s minimum quota. (These calculations are shown in the fourth row of the table below) Find the sum total of the managers so obtained. You will find that one manager is left to be apportioned. Store A B C D Total Sales 2.5 7.6 3.9 5.5 19.5 Standard quota 2.5 0.78 = 3.21 7.6 0.78 = 9.74 3.9 0.78 = 5 5.5 0.78 = 7.05 25 Minimum quota 3 9 5 7 24 Part (a): Hamilton’s Method of apportionment Find each store’s fractional remainder – fraction that remains in the standard quota after subtracting the minimum quota. Give extra manager to the store with highest fractional remainder. (These calculations are shown in the fifth row of the table below) The final apportionment is given in the sixth row of the table below: Store A B C D Total Sales 2.5 7.6 3.9 5.5 19.5 Standard quota 2.5 0.78 = 3.21 7.6 0.78 = 9.74 3.9 0.78 = 5 5.5 0.78 = 7.05 25 Minimum quota 3 9 5 7 24 Fractional remainder 0.21 0.74 (largest) 0.00 0.05 1 Final Apportionment 3 10 5 7 25 Thus, the apportionment of managers to Boulder, Denver, Broomfield and Collins are 3, 10, 5 and 7 respectively. Part (b): Jefferson’s Method of apportionment Since, there is one extra manager, so according to this method you have to choose a modified divisor that is lower than the standard divisor. The store sale is divided by modified divisor to find modified quota. Round these modified quotas to find new set of minimum quotas. The last row in the table below shows the new minimum quotas with a modified divisor of 0.76. Observe that this new set of minimum quota uses all 25 managers. Hence, the last row is the final apportionment. Store A B C D Total Sales 2.5 7.6 3.9 5.5 19.5 Standard quota 2.5 0.78 = 3.21 7.6 0.78 = 9.74 3.9 0.78 = 5 5.5 0.78 = 7.05 25 Minimum quota 3 9 5 7 24 Modified quota 2.5 0.76 = 3.29 7.6 0.76 = 10 3...

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

7th Edition

ISBN: 9780134705187

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Question

Chapter 12.C, Problem 45E

To determine

There are five parts to be determined in this question and these are:

(a) To find apportionment using Hamilton’s method.

(b) To find apportionment using Jefferson’s method.

(c) To find apportionment using Webster’s method.

(d) To find apportionment using Hill-Huntington’s method.

(e) Compare results of various methods

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Chapter 12.C, Problem 44E

Chapter 12.C, Problem 46E

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Chapter 12 Solutions

Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)

Ch. 12.A - Prob. 1QQ Ch. 12.A - Prob. 2QQ Ch. 12.A - Prob. 3QQ Ch. 12.A - Prob. 4QQ Ch. 12.A - Prob. 5QQ Ch. 12.A - Prob. 6QQ Ch. 12.A - Prob. 7QQ Ch. 12.A - Prob. 8QQ Ch. 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. 2E Ch. 12.A - What is a filibuster? What percentage of the vote...Ch. 12.A - Prob. 4E Ch. 12.A - Prob. 5E Ch. 12.A - Prob. 6E Ch. 12.A - Prob. 7E Ch. 12.A - Prob. 8E Ch. 12.A - Prob. 9E Ch. 12.A - Prob. 10E Ch. 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. 14E Ch. 12.A - Prob. 15E Ch. 12.A - Prob. 16E Ch. 12.A - Prob. 17E Ch. 12.A - Prob. 18E Ch. 12.A - Prob. 19E Ch. 12.A - Presidential Elections. The following tables give...Ch. 12.A - Prob. 21E Ch. 12.A - Prob. 22E Ch. 12.A - Prob. 23E Ch. 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. 27E Ch. 12.A - Prob. 28E Ch. 12.A - Prob. 29E Ch. 12.A - Prob. 30E Ch. 12.A - Prob. 31E Ch. 12.A - Prob. 32E Ch. 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. 36E Ch. 12.A - Prob. 37E Ch. 12.A - Prob. 38E Ch. 12.A - Prob. 39E Ch. 12.A - Prob. 40E Ch. 12.A - Prob. 41E Ch. 12.A - How Close Was 2016? Consider Table 12.3 which...Ch. 12.A - Prob. 43E Ch. 12.A - Prob. 44E Ch. 12.A - Prob. 45E Ch. 12.A - Prob. 46E Ch. 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. 50E Ch. 12.A - Prob. 51E Ch. 12.A - Prob. 52E Ch. 12.A - Prob. 53E Ch. 12.A - Prob. 54E Ch. 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. 2QQ Ch. 12.B - Prob. 3QQ Ch. 12.B - Prob. 4QQ Ch. 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. 8QQ Ch. 12.B - Which of the following is not an advantage of...Ch. 12.B - Prob. 10QQ Ch. 12.B - Briefly summarize each of the four fairness...Ch. 12.B - Prob. 2E Ch. 12.B - What is approval voting? How is it different from...Ch. 12.B - Prob. 4E Ch. 12.B - Prob. 5E Ch. 12.B - Prob. 6E Ch. 12.B - Prob. 7E Ch. 12.B - Prob. 8E Ch. 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. 12E Ch. 12.B - Plurality and Criterion 4. Suppose the plurality...Ch. 12.B - Prob. 14E Ch. 12.B - Runoff Methods and Criterion 1. Explain in words...Ch. 12.B - Prob. 16E Ch. 12.B - Prob. 17E Ch. 12.B - Sequential Runoff and Criterion 2. Devise a...Ch. 12.B - Prob. 19E Ch. 12.B - Prob. 20E Ch. 12.B - Prob. 21E Ch. 12.B - Prob. 22E Ch. 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. 26E Ch. 12.B - Prob. 27E Ch. 12.B - Prob. 28E Ch. 12.B - Prob. 29E Ch. 12.B - Prob. 30E Ch. 12.B - Prob. 31E Ch. 12.B - Pairwise Comparisons and Criterion 4. Suppose the...Ch. 12.B - Prob. 33E Ch. 12.B - Approval Voting. Suppose that Candidates A and B...Ch. 12.B - Prob. 35E Ch. 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. 39E Ch. 12.B - Prob. 40E Ch. 12.B - Prob. 41E Ch. 12.B - Prob. 42E Ch. 12.B - Prob. 43E Ch. 12.B - Prob. 44E Ch. 12.B - Prob. 45E Ch. 12.B - Prob. 46E Ch. 12.B - Prob. 47E Ch. 12.B - Prob. 48E Ch. 12.B - Prob. 49E Ch. 12.B - Prob. 50E Ch. 12.B - Prob. 51E Ch. 12.B - 52. Swing Votes. Suppose that the following...Ch. 12.B - Prob. 53E Ch. 12.B - Other Fairness Criteria. The fairness criteria...Ch. 12.B - Prob. 55E Ch. 12.B - Power Voting and Coalitions. Use the Web...Ch. 12.B - General Voting Power. Find the news report about...Ch. 12.B - Prob. 58E Ch. 12.C - Prob. 1QQ Ch. 12.C - Prob. 2QQ Ch. 12.C - Prob. 3QQ Ch. 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. 7QQ Ch. 12.C - Prob. 8QQ Ch. 12.C - Prob. 9QQ Ch. 12.C - Prob. 10QQ Ch. 12.C - Prob. 1E Ch. 12.C - Prob. 2E Ch. 12.C - Prob. 3E Ch. 12.C - What is the Alabama paradox? What other paradoxes...Ch. 12.C - Prob. 5E Ch. 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. 11E Ch. 12.C - Prob. 12E Ch. 12.C - Prob. 13E Ch. 12.C - Prob. 14E Ch. 12.C - Prob. 15E Ch. 12.C - Prob. 16E Ch. 12.C - Prob. 17E Ch. 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. 21E Ch. 12.C - Prob. 22E Ch. 12.C - Prob. 23E Ch. 12.C - Prob. 24E Ch. 12.C - Prob. 25E Ch. 12.C - Prob. 26E Ch. 12.C - Prob. 27E Ch. 12.C - Prob. 28E Ch. 12.C - Prob. 29E Ch. 12.C - Prob. 30E Ch. 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. 35E Ch. 12.C - Prob. 36E Ch. 12.C - Prob. 37E Ch. 12.C - Prob. 38E Ch. 12.C - Comparing Methods. Assume 100 delegates are to be...Ch. 12.C - Prob. 40E Ch. 12.C - Prob. 41E Ch. 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. 46E Ch. 12.C - Prob. 47E Ch. 12.C - Prob. 48E Ch. 12.C - Prob. 49E Ch. 12.D - Prob. 1QQ Ch. 12.D - Prob. 2QQ Ch. 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. 5QQ Ch. 12.D - Prob. 6QQ Ch. 12.D - Prob. 7QQ Ch. 12.D - Prob. 8QQ Ch. 12.D - Prob. 9QQ Ch. 12.D - Prob. 10QQ Ch. 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. 8E Ch. 12.D - Polls show that half voters in our state plan to...Ch. 12.D - Prob. 10E Ch. 12.D - Prob. 11E Ch. 12.D - Prob. 12E Ch. 12.D - Redistricting and House Elections. The 2010 census...Ch. 12.D - Prob. 14E Ch. 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. 19E Ch. 12.D - Prob. 20E Ch. 12.D - 18—23: Average and Extreme Districts. Consider the...Ch. 12.D - Average and Extreme Districts. Consider the...Ch. 12.D - Prob. 23E Ch. 12.D - Prob. 24E Ch. 12.D - Prob. 25E Ch. 12.D - Prob. 26E Ch. 12.D - Prob. 27E Ch. 12.D - Prob. 28E Ch. 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. 32E Ch. 12.D - Prob. 33E Ch. 12.D - Prob. 34E Ch. 12.D - Prob. 35E Ch. 12.D - Prob. 36E Ch. 12.D - Prob. 37E Ch. 12.D - Prob. 38E Ch. 12.D - Prob. 39E Ch. 12.D - Prob. 40E Ch. 12.D - Prob. 41E Ch. 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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