Explanation Given: The bureau has ten seats and the given table is, State Michigan Wisconsin Minnesota Population 9 , 883 , 640 5 , 686 , 986 5 , 303 , 925 Procedure: To express the number in term of millions, Divide the number by 1000000, the number obtained is in the term of millions. Consider the number A , So the number is in the thousand is, A ( in millions ) = A 1000000 Standard divisor states that, It is the ratio of the total population to the total number of seats. d = total population total number of seats Modified quota states that, It is the ratio of the state’s population to the modified divisor. q m = state's population modified divisor = state's population d m Modified divisor is less than the standard divisor, d m < d . Round off the standard quota in two decimal places. Lower quota define as, It is the whole number part of standard quota (round down). Steps of Jefferson’s Method of Apportionment is defined as, Step 1: Calculate the standard quotas and the lower quotas by using the standard divisor. Step 2: If the total lower quota is equal to the total seats to be apportioned, then the apportionment process is completed. Step 3: If the total lower quotas not equal to total seats to be apportionment, then choose modified divisor less than standard divisor, d m < d , and calculate the modifier quotas and lower modifier quotas. Step 4: Repeat step3 until modified lower quotas is equal to the total seats of apportionment. Calculation: Consider the given table, State Michigan Wisconsin Minnesota Population 9 , 883 , 640 5 , 686 , 986 5 , 303 , 925 Now, express the state is in millions. State Michigan is in millions, Michigan ( in millions ) = 9883640 1000000 = 9.88 State Wisconsin is in millions, Wisconsin ( in millions ) = 5686986 1000000 = 5.67 State Minnesota is in millions, Minnesota ( in millions ) = 5303925 1000000 = 5.30 So, the table which shows the states is in terms of million. State Michigan Wisconsin Minnesota Population (in millions) 9.88 5.69 5.30 The bureau has ten seats. The total number of population is, 9.88 + 5.69 + 5.30 = 20.87 Now, apply standard divisor formula. d = 20 To determine (b) To find: The apportionment of legislative of seats by using Adams’s Method for the given condition. To determine (c) To find: The apportionment of legislative of seats by using Webster’s Method for the given condition.

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Chapter 6.2, Problem 20E

To determine

(a)

To find:

The apportionment of legislative of seats by using Jefferson’s Method for the given condition.

To determine

(b)

To find:

The apportionment of legislative of seats by using Adams’s Method for the given condition.

To determine

(c)

To find:

The apportionment of legislative of seats by using Webster’s Method for the given condition.

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Chapter 6 Solutions

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Ch. 6.1 - Four candidates, Alliotti, Baker, Cruz, and Daud,...Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Number of Ballots Cast 6 8 7 10 15 1st choice C C...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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(a) To find: The apportionment of legislative of seats by using Jefferson’s Method for the given condition.

Solution Summary: The author explains the apportionment of legislative of seats by using Jefferson's Method for the given condition.

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(a) To find: The apportionment of legislative of seats by using Jefferson’s Method for the given condition.

(b) To find: The apportionment of legislative of seats by using Adams’s Method for the given condition.

(c) To find: The apportionment of legislative of seats by using Webster’s Method for the given condition.

Chapter 6 Solutions

(a)

To find:

The apportionment of legislative of seats by using Jefferson’s Method for the given condition.

(b)

To find:

The apportionment of legislative of seats by using Adams’s Method for the given condition.

(c)

To find:

The apportionment of legislative of seats by using Webster’s Method for the given condition.