Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Question
Chapter 2, Problem 3E
To determine
(a)
To calculate:
The smallest value that the can be taken by quota
To determine
(b)
To calculate:
The largest value that the can be taken by quota
To determine
(c)
To calculate:
The value of the quota if at least three-fourths of the votes are required to pass a motion.
To determine
(d)
To calculate:
The value of the quota if more than three-fourths of the votes are required to pass a motion.
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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:
Which is the correct answer to the question.
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...
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