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 13E
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.
75 seats are apportioned.
| State | Original State a | Original State b | New State c |
| Population | 3184 | 8475 | 330 |
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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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 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_forwardWhich one of the apportionment methods studied does not violate the quota rule? Group of answer choices Hamilton's Method Jefferson's Method Adam's Method Webster's Methodarrow_forward
- Use Adams'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.arrow_forwardConsider the apportionment of 40 doctors for a physicians organization. The apportionment using Hamilton's method is shown in the table below. Does the Alabama paradox occur using Hamilton's method if the number of doctors is increased from 40 to 41? Clinic A E Total Patients 246 201 193 207 224 1071 Standard quota Lower quota 9.19 7.51 7.21 7.73 8.36 40.00 7 7 7 38 Hamilton's 8 7 8 40 apportionment Complete the table below with the new apportionment for clinics A, B, C, D, and E using a standard divisor rounded to two decimal places. Clinic A E Total Patients 246 201 193 207 224 1071 Hamilton's apportionment 41arrow_forwardPlease help me with this ASAParrow_forward
- Consider the apportionment of 50 doctors for a physicians organization. The apportionment using Hamilton's method is shown in the table below. Does the Alabama paradox occur using Hamilton's method if the number of doctors is increased from 50 to 51? Clinic Patients Standard quota Lower quota Hamilton's apportionment A 656 Clinic Patients Hamilton's apportionment 11.44 11 12 B 536 9.35 9 9 656 O C 525 9.16 9 9 536 525 D 555 Complete the table below with the new apportionment for clinics A, B, C, D, and E using a standard divisor rounded to two decimal places. - 9.68 9 10 E 595 D 555 10.38 10 10 Total D 2867 50.01 48 50 E 595 Total 2867arrow_forwardAlabama 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_forward
- A 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_forwardplease help me fast....arrow_forward2. What is violated if three unassigned seats are all given to just one state after the Hamilton method of apportionment is applied? Apportionment Principle Relative Unfairness of Apportionment Quota Rule Absolute Unfairness of Apportionmentarrow_forward
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