Mathematical Excursions (MindTap Course List)
4th Edition
ISBN: 9781305965584
Author: Richard N. Aufmann, Joanne Lockwood, Richard D. Nation, Daniel K. Clegg
Publisher: Cengage Learning
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Chapter 4.3, Problem 13ES
To determine
(a)
What is the dictatorship from the given voting systems?
To determine
(b)
What is the veto power system from the given voting systems?
To determine
(c)
What is the null systems?
To determine
(d)
What is the one person, one vote system?
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The legislature in a state has 31 seats. Apportion these seats to the five counties below using Jefferson's method.
County
Population
Seats Received
Adams
194,000
Grant
262,000
Colton
356,000
Davis
98,000
Hayes
269,000
The legislature in a state has 36 seats. Apportion these seats to the five counties below using Hamilton's method.
County
Population
Seats Received
Adams
186,000
Grant
329,000
Colton
465,000
Davis
441,000
Hayes
176,000
Here are the results of the voting by eight senators on voting by three bills in the U.S. Senate during the 107th Congress, second session (2002):
Senator
Bill A
Bill B
Bill C
S. 2414
H.R. 2356
Amen. 3017
Clinton (D)
yea
yea
yea
Kennedy (D)
yea
yea
yea
Bayh (D)
nay
yea
nay
Inouye (D)
yea
yea
nay
Campbell (R)
yea
nay
nay
Helms (R)
yea
nay
nay
Thurmond (R)
yea
nay
nay
Lott (R)
yea
nay
nay
Assign each senator to the appropriate region of the figure below. A "yea" vote is recorded as supporting the bill and consequently places the senator inside the circle representing that particular bill.
Clinton
Kennedy
Bayh
Inouye
Campbell
Helms
Thurmond
Lott
Chapter 4 Solutions
Mathematical Excursions (MindTap Course List)
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. 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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
- Here are the results of the voting by eight senators on voting by three bills in the U.S. Senate during the 107th Congress, second session (2002): Senator Bill A Bill B Bill C S. 2414 H.R. 2356 Amen. 3017 Clinton (D) yea yea yea Kennedy (D) yea yea yea Bayh (D) nay yea nay Inouye (D) yea yea nay Campbell (R) yea nay nay Helms (R) yea nay nay Thurmond (R) yea nay nay Lott (R) yea nay nay Assign each senator to the appropriate region of the figure below. A "yea" vote is recorded as supporting the bill and consequently places the senator inside the circle representing that particular billarrow_forwardThe legislature in a state has 48 seats. Apportion these seats to the five counties below using Lowndes' method. County Population Seats Received Adams 382,000 Grant 245,000 Colton 457,000 Davis 491,000 Hayes 72,000arrow_forwardThe legislature in a state has 59 seats. Apportion these seats to the six counties below using the Huntington-Hill method. County Population Seats Received Adams 196,000 Grant 173,000 Colton 150,000 Davis 193,000 Hayes 232,000 McKinley 477,000arrow_forward
- 1) find the mode of regions for the states that voted for the Democratic and for the Republic respectively and explain the findings.arrow_forwardUsing Webster's Method, if the modified quota is 50,100 and the population for State J is 1, 646,000, then the exact number of seats to be apportioned for State J is Group of answer choices 33 34 31 32arrow_forwardDetermine whether any of the listed candidates has a majority. Four candidates running for mayor receive votes as follows. Ito: 40,761 Johnson 18,116 Kennedy:9,058 Lieberman 13,587arrow_forward
- In the United States, each national federation has the authority to determine the means for how it selects participants for world championships and for submission to become members of the Olympic team. True Falsearrow_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_forwardThe following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or sixth grade. Number of Teachers Number of Students Fifth Grade 20 576 Sixth Grade 23 726 (a) Use the apportionment principle to determine to which grade the new teacher should be assigned. fifth gradesixth grade (b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned. fifth gradesixth grade How does this result compare with the result in part (a)? same resultdifferent resultarrow_forward
- Consider the apportionment of 60 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 60 to 61? Clinic A B C D E Total Patients 656 536 515 549 602 2858 Standard quota 13.77 11.25 10.81 11.53 12.64 60.00 Lower quota 13 11 10 11 12 57 Hamilton's apportionment 14 11 11 11 13 60 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 B C D E Total Patients 656 536 515 549 602 2858 Hamilton's apportionment ? ? ? ? ? 61arrow_forwardIn the apportionment of the House of Representatives based on the 1790 Census, there are 15 states. At that time Maine was still considered part of Massachusetts. If Maine had been a separate state, it would have shared in the distribution of the seats in the House. In the 1790 census, Maine's population was 96,643. Subtract this number from Massachusetts' population and then answer the question .State_______________ Population Connecticut_______ 237,655 Delaware______________59,096 Georgia_________________82,548 Kentucky_______________73,677 Maryland_______________319,728 Massachusetts___________475,199 New Hampshire___________141,899 New Jersey_________________184,139 New York__________________340,241 North Carolina______________395,005 Pennsylvania________________433,611 Rhode Island__________________69,112 South Carolina______________249,073 Vermont_____________________85,341 Virginia______________________747,550 TOTAL_______________________3,893,874 What are the standard quotas…arrow_forwardConsider the apportionment of 27 projectors for a school district with four campus locations labeled A, B, C, and D. The following table shows the apportionment of the projectors using the Hamilton method. Campus A B C D Enrollment 840 1942 320 2760 Apportionment of 27 projectors 4 9 1 13 (a) If the number of projectors to be apportioned increases from 27 to 28, what will be the apportionment if the Hamilton method is used? Campus A Campus B Campus C Campus D Did the Alabama paradox occur? YesNo (b) If the number of projectors to be apportioned using the Hamilton method increases from 28 to 29, will the Alabama paradox occur? YesNoarrow_forward
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