Excursions in Modern Mathematics, Books a la carte edition (9th Edition)
9th Edition
ISBN: 9780134469041
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 2, Problem 71E
To determine
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The player
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A voter who has a weight that is greater than or equal to the quota is called a dictator. In a weighted voting system, the dictator has all the power. A voter who is never a critical voter has no power and is referred to as a dummy. This term is not meant to be a comment on the voter’s intellectual powers; it just indicates that the voter has no ability to influence an election.
a. dictators : v1,v2 ; dummies : v2,v3
b. dictator : v1; dummies : v2,v3,v4,v5
c. dictator : v1; dummy : v2
d. The system is not valid.
Problem:Allocate 25 seats for five states whose populations are 12576, 13146, 14105, 13578, and 12986 respectively using
1. The Hamilton Method
Problem:Allocate 25 seats for five states whose populations are 12576, 13146, 14105, 13578, and 12986 respectively using
The Adams Method
Chapter 2 Solutions
Excursions in Modern Mathematics, Books a la carte edition (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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- Problem:Allocate 25 seats for five states whose populations are 12576, 13146, 14105, 13578, and 12986 respectively using The Huntington-Hill Method PreviousNextarrow_forwardA chapter of the Sierra Club is voting for president. The candidates are (A)lvaro, (B)rown, (C)lark, and (D)ukevitch. Number of Ballots 4 23 8 3 12 1st preference C D C A A 2nd preference A A B D B 3rd preference B B D B C 4th preference D C A C D Show that Condorcet’s criterion is not satisfied when the Borda count method is used in this casearrow_forwardA group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (BCA) (ACB) (CAB) 10 4 5 Who wins the election using the Hare method? Does this violate the Condorcet criterion?arrow_forward
- A company has 30,000 employees in three cities as shown in the table below. It wishes to give promotions to 200 employees. Cities A B C Total Original Number of Employees 9150 6070 14,780 30,000 a) Apportion the promotions using Hamilton's method. b) Suppose that in 10 years the cities have the following number of employees and the company wishes to again give promotions to 200 employees. Does the population paradox occur using Hamilton's method? Cities A B C Total Number of Employees 10 years later 9190 6070 14,915 30,175 a) Complete the table with Hamilton's apportionment for the original number of employees. Cities A B C Total Original Number of Employees 9150 6070 14,780 30,000 Hamilton's Apportionment enter your response here enter your response here enter your response here 200arrow_forwardConsider the weighted voting system [Q: 7, 5, 3]. Which of the following options for Q would create a valid system where player 1 has veto power without being a dictator? Group of answer choices Q=7 Q=9 No value of Q meet these criteria. Q=8arrow_forwardsuppose and electronics company has three divisions D digital C computers and B business products division D has 142 employees see has 84 and B has 27 assume that 12 member quality improvement counsel has membership on the council proportional to the number of employees in the three divisions a. apportion this council using Hamilton method b. now increase the councils size to 13 and then to 14 and apportion this council using Hamilton method. c. what is the first size above 12 when the Alabama paradox, occurs, and what division loses a seat when the size of the council increases.arrow_forward
- Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Mutiple Choice:a. No b. Yesarrow_forwardConsider the weighted voting system [q: 9, 5, 1].Which values of q result in a dictator (list all possible values)What is the smallest value for q that results in exactly one player with veto power who is not a dictator?What is the smallest value for q that results in exactly two players with veto power?arrow_forwardA group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) (CBA) (BCA) 6 10 9 Who wins using the Borda count method? Does this violate the Condorcet criterion?arrow_forward
- the comic book store owner is curious in how well radio and newspaper advertisements work. A sample of 22 counties with almost equal populations was gathered during the month. For each of the counties, the owner has set aside a particular sum for radio and newspaper advertising. Additionally, the owner was able to access comic book sales information for the stores he controlled in each county and classified it as Low or High. COUNTY (X1) Comic book Sales (X2) (0 = Low, 1 = High) Radio Ads (X3) (in thousands) Newspaper Ads (X4) (in thousands) 1 1 0 40 2 0 0 40 3 0 25 25 4 0 25 25 5 0 30 30 6 0 30 30 7 0 35 35 8 0 35 35 9 0 40 25 10 0 40 25 11 1 45 45 12 1 45 45 13 1 50 0 14 1 50 0 15 1 55 25 16 1 55 25 17 1 60 30 18 1 60 30 19 1 65 35 20 1 65 35 21 1 70 40 22 1…arrow_forwardthe comic book store owner is curious in how well radio and newspaper advertisements work. A sample of 22 counties with almost equal populations was gathered during the month. For each of the counties, the owner has set aside a particular sum for radio and newspaper advertising. Additionally, the owner was able to access comic book sales information for the stores he controlled in each municipality and classified it as Low or High. COUNTY (X1) Comic book Sales (X2) (0 = Low, 1 = High) Radio Ads (X3) (in thousands) Newspaper Ads (X4) (in thousands) 1 1 0 40 2 0 0 40 3 0 25 25 4 0 25 25 5 0 30 30 6 0 30 30 7 0 35 35 8 0 35 35 9 0 40 25 10 0 40 25 11 1 45 45 12 1 45 45 13 1 50 0 14 1 50 0 15 1 55 25 16 1 55 25 17 1 60 30 18 1 60 30 19 1 65 35 20 1 65 35 21 1 70 40 22…arrow_forward
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