Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
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Textbook Question
Chapter 15.4, Problem 14E
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 | 350 |
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
Jefferson's method, Webster's method, and Adams's method require using a _______ quota.
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 doctors
Use 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
State
E
F
Total
Standard Divisor
Modified Divisor
200
Population Standard Rounded Modified
Quotas
Up
Quotas
Quotas
1,598,400
1,236,300
5,460,200
826,900
965,500
1,112,700
11,200,000
Modified
Upper
Quotas
Chapter 15 Solutions
Mathematical Ideas (13th Edition) - Standalone book
Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by the Plurality Method A...Ch. 15.1 - Choosing a Poster Dog by Alternative Methods For...Ch. 15.1 - Choosing a Poster Dog by Alternative MethodsFor...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...Ch. 15.1 - Observing the Effect of the Number of Candidates...
Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Applying Four Voting Methods to a Voter Profile...Ch. 15.1 - Holding a Runoff Election One common solution to...Ch. 15.1 - Prob. 20ECh. 15.1 - Prob. 21ECh. 15.1 - Prob. 22ECh. 15.1 - Prob. 23ECh. 15.1 - Prob. 24ECh. 15.1 - Prob. 25ECh. 15.1 - Prob. 26ECh. 15.1 - Prob. 27ECh. 15.1 - The Pairwise Comparison Method Each table...Ch. 15.1 - Prob. 29ECh. 15.1 - Prob. 30ECh. 15.1 - The Borda Method Each table represents a Borda...Ch. 15.1 - Prob. 32ECh. 15.1 - Prob. 33ECh. 15.1 - Prob. 34ECh. 15.1 - Prob. 35ECh. 15.1 - Prob. 36ECh. 15.1 - The Coombs Method The Coombs method of voting is a...Ch. 15.1 - Prob. 38ECh. 15.1 - Prob. 39ECh. 15.1 - Prob. 40ECh. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Majority...Ch. 15.2 - Identifying Violations of the Majority Criterion...Ch. 15.2 - Identifying Violations of the Condorcet...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Identifying Violations of the Condorcet Criterion...Ch. 15.2 - Prob. 9ECh. 15.2 - Prob. 10ECh. 15.2 - Prob. 11ECh. 15.2 - Prob. 12ECh. 15.2 - Prob. 13ECh. 15.2 - Prob. 14ECh. 15.2 - Prob. 15ECh. 15.2 - Prob. 16ECh. 15.2 - Prob. 17ECh. 15.2 - Prob. 18ECh. 15.2 - Prob. 19ECh. 15.2 - Irrelevant Alternatives in a Hare Method Election...Ch. 15.2 - 21. Explain why a violation of the majority...Ch. 15.2 - Prob. 22ECh. 15.2 - Prob. 23ECh. 15.2 - Prob. 24ECh. 15.2 - Prob. 25ECh. 15.2 - Prob. 26ECh. 15.2 - Prob. 27ECh. 15.2 - Prob. 28ECh. 15.2 - Prob. 29ECh. 15.2 - Prob. 30ECh. 15.2 - Prob. 31ECh. 15.2 - Prob. 32ECh. 15.2 - Prob. 33ECh. 15.2 - Prob. 34ECh. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Find each quantity (to the nearest whole number)...Ch. 15.3 - Solve each problem.
5. New Trees for Wisconsin...Ch. 15.3 - Apportioning Computers to Schools Enrollments for...Ch. 15.3 - Assigning Faculty to Courses The English...Ch. 15.3 - 8. Apportioning Sailboats to Resorts The number of...Ch. 15.3 - Prob. 9ECh. 15.3 - 10. Show that the Webster method apportionment of...Ch. 15.3 - Prob. 11ECh. 15.3 - Prob. 12ECh. 15.3 - Prob. 13ECh. 15.3 - Prob. 14ECh. 15.3 - Prob. 15ECh. 15.3 - Find the Huntington-Hill cutoff point for rounding...Ch. 15.3 - Creating a Profile of School Bus Riders Create a...Ch. 15.3 - Prob. 18ECh. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - The standard quotas rounded up to the nearest...Ch. 15.3 - Prob. 22ECh. 15.3 - Prob. 23ECh. 15.3 - Prob. 24ECh. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Quota Rule Violations with the Jefferson Method In...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Alabama Paradox with the Hamilton Method In each...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - Population Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - New States Paradox with the Hamilton Method In...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Violations of the Quota Rule? For each...Ch. 15.4 - Prob. 20ECh. 15.4 - Prob. 21ECh. 15.4 - Prob. 22ECh. 15.4 - Prob. 23ECh. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - 26. The Jefferson and Adams methods are both...Ch. 15 - How many different complete rankings are possible...Ch. 15 - Prob. 2TCh. 15 - Prob. 3TCh. 15 - Prob. 4TCh. 15 - Prob. 5TCh. 15 - Why is the irrelevant alternatives criterion an...Ch. 15 - Prob. 7TCh. 15 - Prob. 8TCh. 15 - Prob. 9TCh. 15 - Prob. 10TCh. 15 - Prob. 11TCh. 15 - Prob. 12TCh. 15 - Prob. 13TCh. 15 - Prob. 14TCh. 15 - Prob. 15TCh. 15 - Prob. 16TCh. 15 - Prob. 17TCh. 15 - Prob. 18TCh. 15 - Prob. 19TCh. 15 - Prob. 20TCh. 15 - Prob. 21TCh. 15 - Prob. 22TCh. 15 - Prob. 23TCh. 15 - Prob. 24TCh. 15 - Prob. 25TCh. 15 - One hundred seats are to be apportioned to 4...Ch. 15 - Prob. 27TCh. 15 - Prob. 28TCh. 15 - Prob. 29TCh. 15 - Explain the Alabama paradox.Ch. 15 - Prob. 31TCh. 15 - Prob. 32T
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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
- Use 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_forwardUse 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_forward
- Consider 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_forward3. 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_forward
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