Mathematical Ideas (13th Edition) - Standalone book
13th Edition
ISBN: 9780321977076
Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 15.4, Problem 4E
Quota Rule Violations with the Jefferson Method In each case, show that if the Jefferson method of apportionment is used, then a violation of the quota rule occurs.
150 seats are apportioned.
| State | a | b | c | d | e |
| Population | 1720 | 3363 | 6960 | 24,223 | 8800 |
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
please help me fast....
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
2867
nts
The legislature in a state has 33 seats. Apportion these seats to the five counties below using Jefferson's
method.
County Population Seats Received
Adams 454,000
44
Grant 383,000
ine E-
Colton 216,000
ordings
Davis 482,000
Hayes 325,000
Question Help: Video
Submit Question
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
Knowledge Booster
Learn more about
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
- Jefferson's method, Webster's method, and Adams's method require using a _______ quota. arrow_forwardDevarrow_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 Patients Standard quota Lower quota Hamilton's apportionment A 492 9.09 9 9 Clinic Patients Hamilton's apportionment B 402 7.43 7 8 с 394 7.28 7 7 B 402 D 424 7.83 7 8 C 394 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. A E 453 492 E 453 8.37 8 8 D 424 Total 2165 40.00 38 40 D Total 2165 41arrow_forward
- SC Find the apportionment asked for. Show your work either by hand or Microsoft Excel (attach your work). 9) A small city has 50 police officers to be apportioned among 8 precincts based on the population of each precinct. The populations are given in the following table. Precinct total 25,95 4 6. 7 8 Population 2250 3800 3225 1800 4900 4025 2775 3175 a) Find the apportionment for each state using Hamilton's method. A COnd dour b) Find the apportionment for each state using Jefferson's method. round down to nearest round up nearest in c) Find the apportionment for each state using Webster's method. round UD d) Find the apportionment for each state using Adams' method.arrow_forwardThe table shows the county's populations after a 2020 census. Complete the table using Hamilton's method to apportion the 30 seats for the populations after 2000. 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. Find the divisor. Enter your answer in the space provided below. Divisor: State Population Standard Initial Quotas Final Quotas 2000 Quotas 43,913 72,543 168,244 284,700 А B C Totalarrow_forwardA small country consists of four states, whose populations are listed below. If thelegislature has 116 seats, apportion the seats using Hamilton’s method. Does thisillustrate any apportionment issues?A: 33,700 B: 559,500 C: 141,300 D: 89,100arrow_forward
- A newly established country has 4 states, A, B, C, and D. Their populations are in the table. The states share 120 representatives. The governors of these states agree that the seats should be apportioned using Adam’s method of apportionment. What is the sum of the first upper quota for the four states?arrow_forwardThe 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_forward4. Find the apportionment under the Jefferson method if there are 100 seats to be apportioned. Hint: The standard divisor is 3,000. State Population Final Apportionment A 67,200 B 78,300 C 73,800 D 80,700arrow_forward
- A small country is comprised of five states, A, B, C, D, and E. The population of each state is given in the following table. Congress will have 58 seats divided among the five states according to their respective populations. Use Jefferson's method with d = 32,920 to apportion 58 seats. State A B D E Population 138,432 218,282 401,379 524.915 714,634 ..... State Number of Apportioned Seats A (Type an integer.)arrow_forwardRecall that the Bandana Republic is apportioning M=160 congressional seats among four states. The states' populations are shown in the table below. Apure Barinas Carabobo Dolores Population 3,310,000 2,670,000 1,330,000 690,000 Find the apportionment under Webster's method of the Bandana Republic Congress. Apure gets Answer seats, Barinas gets Answer seats, Carabobo gets Answer seats, and Dolores gets Answer.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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSON
Discrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
UG/ linear equation in linear algebra; Author: The Gate Academy;https://www.youtube.com/watch?v=aN5ezoOXX5A;License: Standard YouTube License, CC-BY
System of Linear Equations-I; Author: IIT Roorkee July 2018;https://www.youtube.com/watch?v=HOXWRNuH3BE;License: Standard YouTube License, CC-BY