Explanation Given: Total 100 delegates are to be apportioned among three states A, B, C and D with populations 836, 2703, 2626 and 3835 respectively. Formula Used: Standard divisor = total population number of delegates Standard quota = state population standard divisor Calculations: Number of delegates to be apportioned = 100 Total population of the four states = 836 + 2703 + 2626 + 3835 = 10000 Calculate standard divisor Standard divisor = 10000 100 = 100 Calculate Standard quota for each state Standard quota = state population 100 (These calculations are shown in the third row of the table below) 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) Find the sum total of the delegates so obtained. You will find that one delegate is left to be apportioned. State A B C D Total Population 836 2703 2626 3835 10000 Standard quota 836 100 = 8.36 2703 100 = 27.03 2626 100 = 26.26 3835 100 = 38.35 100 Minimum quota 8 27 26 38 99 Part (a): Hamilton’s Method of apportionment Find each state’s fractional remainder – fraction that remains in the standard quota after subtracting the minimum quota. Give extra delegate to the state 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: State A B C D Total Population 836 2703 2626 3835 10000 Standard quota 836 100 = 8.36 2703 100 = 27.03 2626 100 = 26.26 3835 100 = 38.35 100 Minimum quota 8 27 26 38 99 Fractional remainder 0.36 (largest) 0.03 0.26 0.35 1 Final Apportionment 9 27 26 38 100 Thus, the apportionment to the four states A, B, C and D are 9, 27, 26 and 38 respectively. Part (b): Jefferson’s Method of apportionment Since, there is one extra seat, so according to this method you have to choose a modified divisor that is lower than the standard divisor. The state population 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 98.3. Observe that this new set of minimum quota uses all 100 seats. Hence, the last row is the final apportionment. State A B C D Total Population 836 2703 2626 3835 10000 Standard quota 836 100 = 8.36 2703 100 = 27.03 2626 100 = 26.26 3835 100 = 38.35 100 Minimum quota 8 27 26 38 99 Modified quota 836 98.3 = 8.50 2703 98.3 = 27.49 2626 98.3 = 26.71 3835 98.3 = 39.01 101.71 Minimum quota 8 27 26 39 100 Thus, the apportionment to the four states A, B, C and D are 8, 27, 26 and 39 respectively...

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 12.C, Problem 41E

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 40E

Chapter 12.C, Problem 42E

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Chapter 12 Solutions

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th 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...

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