Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 2, Problem 70E
To determine
(a)
To find:
The weighted voting system for the given statement.
To determine
(b)
To find:
The Shapley-Shubik power distribution for the Fresno City Council.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
↑
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial
officer (CFO). It must also appoint a planning committee with five different members. There are 14 qualified candidates,
and officers can also serve on the committee. Complete parts (a) through (c) below.
a. How many different ways can the officers be appointed?
different ways to appoint the officers.
b. How many different ways can the committee be appointed?
There are different ways to appoint the committee.
c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified
candidates?
There are
P(getting the five youngest of the qualified candidates) =
(Type an integer or a simplified fraction.)
CHAPTER IX - Apportionment and Voting -
The following table shows the enrollment for each of the four divisions of a
3.
college. The four divisions are liberal arts, business, humanities, and
science. The are 150 new computers that are to be apportioned among the
divisions based on the enrollment.
Division
Enrollment
Liberal arts
1234
Business
3470
Humanities
1825
Science
4052
Total
10, 581
a. What is the standard divisor for an apportionment of the computers?
What is the meaning of the standard divisor in the of this exercise?
b. Use the Hamilton method to determine the number of computers to be
apportioned to each division.
c. If the computers are to be apportioned using the Jefferson method,
explain why neither 70 nor 68 can be used as a modified standard
divisor. Explain why 69.5 can be used as a modified standard divisor.
d. Explain why the modified standard divisor used in the Jefferson method
cannot be larger than the standard divisor.
e. Use the Jefferson method to determine…
A small country consists of seven states; there are 160 seats in the legislature
that need to be apportioned among the seven states; and the population of each
state is shown in the table.
A B C
D E
F G
Population 1283 2374 2725 2155 1592 2511 2017
State
Does the Alabama paradox occur using Hamilton's method if the number of
seats is increased from 160 to 161?
Select one:
a. No
O b. Yes
Chapter 2 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Five partners (P1,P2,P3,P4, andP5) jointly own the...Ch. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - In each of the following weighted voting systems,...Ch. 2 - In each of the following weighted voting systems,...Ch. 2 - Consider the weighted voting system[q:7,5,3]. Find...Ch. 2 - Consider the weighted voting system...Ch. 2 - A committee has four members (P1,P2,P3,andP4). In...Ch. 2 - A committee has six members...
Ch. 2 - Consider the weighted voting system [q:7,5,3]. a....Ch. 2 - Consider the weighted voting system...Ch. 2 - Find the Banzhaf power distribution of a weighted...Ch. 2 - Find the Banzhaf power distribution of a weighted...Ch. 2 - Consider the weighted voting system [10:6,5,4,2]....Ch. 2 - Consider the weighted voting system [5:3,2,1,1]....Ch. 2 - a.Find the Banzhaf power distribution of this...Ch. 2 - a. Find the Banzhaf power distribution of the...Ch. 2 - Consider the weighted voting system [q:5,4,3,2,1]....Ch. 2 - Consider the weighted voting system [q:8,4,2,1]....Ch. 2 - In a weighted voting system with three players the...Ch. 2 - In a weighted voting system with four players the...Ch. 2 - The Nassau County N.Y. Board of Supervisors 1960s...Ch. 2 - The Nassau County N.Y. Board of Supervisors 1960s...Ch. 2 - A law firm is run by four partners (A,B,C,andD)....Ch. 2 - A law firm is run by four partners (A,B,C,andD)....Ch. 2 - Table 2-13 shows the 24 sequential coalitions with...Ch. 2 - Table 2-14 shows the 24 sequential coalitions with...Ch. 2 - Consider the weighted voting system [16:9,8,7]. a....Ch. 2 - Consider the weighted voting system [8:7,6,2]. a....Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - Find the Shapley-Shubik power distribution of each...Ch. 2 - In a weighted voting system with three players the...Ch. 2 - In a weighted voting system with three players the...Ch. 2 - Table 2-15 shows the 24 sequential coalitions in a...Ch. 2 - Table 2-16 shows the 24 sequential coalitions in a...Ch. 2 - Let A be a set with 10 elements. a. Find the...Ch. 2 - Prob. 40ECh. 2 - For a weighted voting system with 10 players. a....Ch. 2 - Consider a weighted voting system with 12 players....Ch. 2 - Consider a weighted voting system with six players...Ch. 2 - Consider a weighted voting system with five...Ch. 2 - Use a calculator to compute each of the following....Ch. 2 - Prob. 46ECh. 2 - Prob. 47ECh. 2 - Prob. 48ECh. 2 - The purpose of Exercises 49 and 50 is for you to...Ch. 2 - The purpose of Exercises 49 and 50 is for you to...Ch. 2 - Consider a weighted voting system with seven...Ch. 2 - Consider a weighted voting system with seven...Ch. 2 - A law firm has seven partners: a senior partner...Ch. 2 - A law firm has six partners: a senior partner (P1)...Ch. 2 - Prob. 55ECh. 2 - Prob. 56ECh. 2 - Consider the weighted voting system [q:8,4,1]. a....Ch. 2 - Consider the weighted voting system [9:w,5,2,1]....Ch. 2 - Equivalent voting systems. Two weighted voting...Ch. 2 - Veto power. A player P with weight w is said to...Ch. 2 - Consider the generic weighted voting system...Ch. 2 - Prob. 62ECh. 2 - Prob. 63ECh. 2 - The weighted voting system [27:10,8,6,4,2]...Ch. 2 - Prob. 65ECh. 2 - Mergers. Sometimes in a weighted voting system two...Ch. 2 - a.Verify that the weighted voting systems...Ch. 2 - Prob. 68ECh. 2 - Prob. 69ECh. 2 - Prob. 70ECh. 2 - Prob. 71ECh. 2 - Prob. 72ECh. 2 - Prob. 73ECh. 2 - Prob. 74ECh. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Suppose that in a weighted voting system there is...Ch. 2 - a. Give an example of a weighted voting system...Ch. 2 - a. Explain why in any weighted voting system with...
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
- In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president, vice president, and treasurer be elected?arrow_forwardChoosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?arrow_forwardCommittee: The Student Council at a certain school has seven members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer. In how many ways can four people be chosen for the executive committee if it does not matter who gets which position?arrow_forward
- Answer a,b, and carrow_forwardA corporation must appoint a president, chief executive officer (CEO), chief operating officer (CO0), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 11 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the officers be appointed? There are different ways to appoint the officers. b. How many different ways can the committee be appointed? There are different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates? P(getting youngest of the qualified candidates) = (Type an integer or a simplified fraction.)arrow_forwardExample: A club has 10 seniors, 7 juniors, 8sophomores, and 5 freshman. How many ways canthe club choose a 6 person planning committee withexactly 3 juniors?arrow_forward
- Six college sorority sisters-Summer, Autumn, Wynter, June, April, and January-got together for their twentieth reunion. Since college they had moved to six different states. Two lived out west (Oregon and Washington), two lived back east (New York and New Hampshire), and two lived down south (Oklahoma and Texas). They all sat around a round table. 1. The Texan sat between Autumn and the woman who lives in New Hampshire. 2. Wynter sat across from April. 3. January sat between Summer and the Washingtonian. 4. June and the woman to her left both live out west. 5. April sat between two easterners. Where does Summer live? Where does January live? Where does Autumn live?arrow_forwardThere are 10 board members on the Community Arts Council. In how many ways can a president and treasurer be chosen? Assume that no member can hold both positions at the same time.arrow_forwardThere are forty-nine ways to select a president and secretary if one person can hold both offices. There are eighteen ways to select a president and a secretary with a female president. There are twenty-four ways to select opposite sex president and secretary. There are 210 ways to select three officers.arrow_forward
- An archaeology club has 34 members. How many different ways can the club select a president, vice president, treasurer, and secretary? There are different slates of candidates possible. (Simplify your answer.)arrow_forwardSeven women and nine men are on the faculty in the mathematics department at a school. How many ways are there to select a committee of five members of the department if at most two men must be on the committee? a. 4032. b. 436. c. 4320. d. 372arrow_forwardCorporate Officers and Committees The Newport Medical Supply Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a strategic planning committee with four different members. There are 10 qualified candidates, and officers can also serve on the committee. a. How many different ways can the four officers be appointed? b. How many different ways can a committee of four be appointed? c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY