Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
1st Edition
ISBN: 9780321977274
Author: Miller, Charles, Heeren, Vern, HORNSBY, John, Christopher
Publisher: PEARSON
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Chapter 15.4, Problem 16E
New States Paradox with the Hamilton Method In each case, use the Hamilton method to apportion legislative seats to two states with the given populations. Show that the new states paradox occurs if a new state with the indicated population and the appropriate number of additional seats is included in a second Hamilton method apportionment. The appropriate number of seats to add for the second apportionment is the state’s standard quota of the new state, computed using the original two-state standard divisor, rounded down to the nearest integer. The populations are given in hundreds.
83 seats are apportioned.
| State | Original State a | Original State b | New State c |
| Population | 7500 | 9560 | 1510 |
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Students have asked these similar questions
Jefferson's method, Webster's method, and Adams's method require using a _______ quota.
There are 3 states and 20 seats. In 20 years, the number of seats was increased to 21.
Suppose the years are 2000 and 2020.
1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations
after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7
decimal places if needed. You can use a spreadsheet to help you figure out an answer or
calculate using a calculator. Fill in every cell.
20 seats
21 seats
State
Population
2000
Standard
Initial
Final
Standard
Initial
Final
Quotas
Quotas
Quotas
Quotas
Quotas
Quotas
5,222
9,677
15,821
30,720
А
B
C
Total
2.) What are the two divisors? Enter your answer in the space provided below.
Divisor for 20 seats:
Divisor for 21 seats:
There are 3 states and 20 seats. In 20 years, the number of seats was increased to 21.
Suppose the years are 2000 and 2020.
1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations
after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7
decimal places if needed. You can use a spreadsheet to help you figure out an answer or
calculate using a calculator. Fill in
every
cell.
20 seats
21 seats
Population
2000
State
Standard
Initial
Final
Standard
Initial
Final
Quotas
Quotas
Quotas
Quotas
Quotas
Quotas
A
5,222
9,677
15,821
30,720
B
Total
2.) What are the two divisors? Enter your answer in the space provided below.
Divisor for 20 seats:
Divisor for 21 seats:
3.) Did an Alabama paradox occur? Explain your answer.
Write your response below:
Chapter 15 Solutions
Mathematical Ideas with Integrated Review and Worksheets plus NEW MyLab Math with Pearson eText -- Access Card Package (Integrated Review Courses in MyLab Math and MyLab Statistics)
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- The apportionment method that requires rounding the standard quota down to the lower quota is called X a. Jefferson's method b. Adams' method c. Webster's method d. Hamilton's method Question 11 A group called Physicians Medical Organization provides 85 medical clinics. The organization has hired 85 doctors. Since the clinics do not serve all the same number of patients, the organization decides to apportion the 85 doctors based on the number of patients who visit each clinic in a given week. Clinic A В C E Total Patients 350 221 205 233 250 1259 Use Hamilton's method for apportionment to determine how many doctors each clinic receives. a. A: 24 doctors, B: 15 doctors, C: 14 doctors, D: 15 doctors, E: 17 doctors X b. A: 23 doctors, B: 14 doctors, C: 13 doctors, D: 15 doctors, E: 16 doctors C. A: 24 doctors, B: 14 doctors, C: 14 doctors, D: 16 doctors, E: 17 doctors d. A: 24 doctors, B: 15 doctors, C: 14 doctors, D: 16 doctors, E: 16 doctorsarrow_forwardUse Adamss's method of apportionment to solve the following problem. 1. Suppose a nation has 6 states, with populations shown in the chart below. The representative body had 200 seats. Find: the standard divisor, the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats 200 Rounded Modified Modified Upper Quotas State Population Standard Quotas Up Quotas Quotas 1,598,400 1,236,300 5,460,200 826,900 965,500 1,112,700 11,200,000 А В C F Total Standard Divisor Modified Divisorarrow_forward5. Name the apportionment method in which we round each group's modified quota to the nearest whole number? 6. Name the paradox. " The addition of a new group changed the apportionments of other groups"arrow_forward
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- 3. Using Jefferson plan method (JP), What leisure activities do you participate in? In the table below are five activities and the approximate number of participants (in millions) in each. EXERCISE 150 SPORTS 90 CHARITY WORK 85 НОМE REPAIR 130 COMPUTER 80 PARTS Suppose you wish to allocate $100 million to pro- mote leisure activities on the basis of the пиmber of partiсіpants. A) Find the modified quota for each activity using the divisor 5.25. B) Find how much money should be apportioned to each activity using Jefferson's method.arrow_forwardUse Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5 states, with populations shown in the chart below. The representative body had 150 seats. Find: the standard divisor, • the modified divisor, and the distribution of representatives to each state. Then complete the table. Round all standard and modified quotas to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Representative Seats 150 State Population Standard Rounded Modified Modified Quotas Quotas Quotas Rounded Quotas A 1,895,500 1,234,500 845,200 399,120 500,680 4,875,000 B D E Total Standard Divisor Modified Divisorarrow_forwardI just need help on question e thank youarrow_forward
- Alabama Paradox There are 3 states and 20 seats. In 20 years, the number of seats was increased to 21. Suppose the years are 2000 and 2020. 1.) Complete the table using Hamilton's method to apportion the 20 seats for the populations after 2000 and the 21 seats after 2020. Round all standard quotas and the divisor to 7 decimal places if needed. You can use a spreadsheet to help you figure out an answer or calculate using a calculator. Fill in every cell. 20 seats 21 seats State Population 2000 Standard Initial Final Standard Initial Final Quotas Quotas Quotas Quotas Quotas Quotas A 5,222 В 9,677 15,821 30,720 C Total 2.) What are the two divisors? Enter your answer in the space provided below. Divisor for 20 seats: Divisor for 21 seats: 3.) Did an Alabama paradox occur? Explain your answer. Write your response below:arrow_forwardHelp me pleasearrow_forwardA small country consists of five states. Call these states A, B, C, D, and E. The standard quotas for each state are given in the table below. (a) Find the number of seats being apportioned. (b) Find the apportionment under the Huntington-Hill rounding rule. State Standard quota 5.27 B C E 14.70 2.66 18.28 19.09 (a) The number of seats being apportioned is (Type a whole number.) (b) Complete the table below. State Standard quota 5.27 A C 14.70 2.66 18.28 19.09 Huntington-Hill (Type whole numbers.) Enter your answer in each of the answer boxes. MacBook Air 20 F1 F2 F3 D0O F4 F5 F7arrow_forward
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