Explanation Given: (a) 100 delegates are to be apportioned among three states A, B and C with populations 5310, 1330 and 3308 respectively. (b) A new state with population of 500 is added and 5 more seats are also added. Formula Used: Standard divisor = total population number of delegates Standard quota = state population standard divisor Calculations: Part (a): Number of delegates to be apportioned = 100 Total population of the three states = 5310 + 1330 + 3308 = 9948 Calculate standard divisor Standard divisor = 9948 100 = 99.48 Calculate Standard quota for each state Standard quota = state population 99.48 (These calculations are shown in the third row of the table below) According to Hamilton’s Method of apportionment, Step1. Give each state the number of delegates 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) Step2. Find each state’s fractional remainder – fraction that remains in the standard quota after subtracting the minimum quota. Give first extra delegate to the state with highest fractional remainder, next to the second highest fractional remainder and so on until all delegates are apportioned. (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: State A B C Total Population 5310 1330 3308 9948 Standard quota 5310 99.48 = 53.38 1330 99.48 = 13.37 3308 99.48 = 33.25 100 Minimum quota 53 13 33 99 Fractional remainder 0.38 (largest) 0.37 0.25 1 Final Apportionment 54 13 33 100 Thus, the apportionment to the three states A, B and C are 54, 13 and 33 respectively. Part (b): Since, a new state with population 500 is added. So, total population of the four states A, B, C and D is Total population = 5310 + 1330 + 3308 + 500 = 10448 Also, 5 more seats were added, so now Number of delegates to be apportioned = 105 Calculate standard divisor Standard divisor = 10448 105 = 99...

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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Chapter 12.C, Problem 38E

To determine

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

(a) To find apportion of 100 delegates among three states using Hamilton’s method.

(b) To find the apportionment of 4 states, when a new state and 5 more seats are added.

(c) To determine if the addition of new state decreases the representation of any of the original states.

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Chapter 12.C, Problem 37E

Chapter 12.C, Problem 39E

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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. 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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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