Math in Our World
3rd Edition
ISBN: 9780073519678
Author: David Sobecki Professor, Allan G. Bluman
Publisher: McGraw-Hill Education
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Chapter 13.1, Problem 15E
To determine
To explain: Whether the head-to-head comparisons criterion violates the results in Exercise 11 or not.
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Consider the weighted voting system [16: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction:
P1:
P2:
P3:
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Consider the weighted voting system [9: 7, 4, 1]Find the Shapley-Shubik power distribution of this weighted voting system.List the power for each player as a fraction:P1: P2: P3:
Chapter 13 Solutions
Math in Our World
Ch. 13.1 - The Student Activities Committee at Camden College...Ch. 13.1 - An election was held for the chairperson of the...Ch. 13.1 - Prob. 3TTOCh. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Explain the head-to head comparison criterion.Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7E
Ch. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Using the election results given in Exercise 9,...Ch. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Using the election results given in Exercise 12,...Ch. 13.1 - Using the Internet as a resource, look up the...Ch. 13.1 - Suppose that an election has seven candidates, and...Ch. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.2 - Prob. 1TTOCh. 13.2 - Prob. 2TTOCh. 13.2 - Prob. 3TTOCh. 13.2 - If the one voter who listed softball last in the...Ch. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Can a candidate that gets the least first-place...Ch. 13.2 - A gaming club holds a vote to decide what type of...Ch. 13.2 - The McKees Point Yacht Club Board of Directors...Ch. 13.2 - Prob. 9ECh. 13.2 - A local police union is holding an election for a...Ch. 13.2 - Students at a college were asked to rank three...Ch. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Does the election in Exercise 12 violate the...Ch. 13.2 - An English department is voting for a new...Ch. 13.2 - The Association of Self-Employed Working Persons...Ch. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Suppose that all 4 voters from the last column of...Ch. 13.2 - Suppose that 2 of the 4 voters from the second...Ch. 13.2 - If 2 of the voters from column 1 in Exercise 21...Ch. 13.2 - If the 3 voters in column 4 in Exercise 22 change...Ch. 13.2 - Construct a preference table for an election...Ch. 13.2 - Construct a preference table for an election...Ch. 13.2 - Construct a preference table for an election so...Ch. 13.2 - If the candidates on a preference ballot are...Ch. 13.2 - If the candidates on a preference ballot are...Ch. 13.2 - In an election with four candidates, how many...Ch. 13.2 - Based on your answers to Exercise 32, explain why...Ch. 13.2 - One way to avoid the issue described in Exercises...Ch. 13.2 - Lets talk about a modified Borda count method....Ch. 13.3 - Prob. 1TTOCh. 13.3 - Prob. 2TTOCh. 13.3 - Does the election in Try This One 2 violate the...Ch. 13.3 - Prob. 4TTOCh. 13.3 - Explain how to determine the winner of an election...Ch. 13.3 - Prob. 2ECh. 13.3 - Describe Arrows impossibility theorem. How is it...Ch. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Which of the five voting methods we studied do you...Ch. 13.3 - If all of the voters in an approval voting...Ch. 13.3 - Fill in the table below, which summarizes our five...Ch. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - The McKees Point Yacht Club Board of Directors...Ch. 13.3 - The students in Dr. Lees math class are asked to...Ch. 13.3 - If Professor Donovan was unable to serve as...Ch. 13.3 - If the travel company from Exercise 14 loses its...Ch. 13.3 - If the West Oak Golf Club is unavailable and the...Ch. 13.3 - If a room for Dr. Lees final exam was not...Ch. 13.3 - A sports committee of students needs to choose a...Ch. 13.3 - Prob. 24ECh. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Construct a preference table so that one candidate...Ch. 13.3 - Prob. 31ECh. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Evaluate each voting method we studied if there...Ch. 13.3 - Suppose that in an election for city council,...Ch. 13.3 - Prob. 36ECh. 13.3 - Devise a method for breaking ties when using...Ch. 13.3 - Prob. 38ECh. 13.4 - Prob. 1TTOCh. 13.4 - Prob. 2TTOCh. 13.4 - Prob. 3TTOCh. 13.4 - Prob. 4TTOCh. 13.4 - Prob. 5TTOCh. 13.4 - Assign the 30 seats from Try This One 5 using...Ch. 13.4 - Prob. 7TTOCh. 13.4 - Prob. 8TTOCh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Describe how to find the upper and lower quotas...Ch. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - In Exercises 912, find the standard divisor for...Ch. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - Prob. 19ECh. 13.4 - Prob. 20ECh. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - For Exercises 2628 find: (a)The standard divisor....Ch. 13.4 - Prob. 27ECh. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.4 - Prob. 32ECh. 13.4 - Prob. 33ECh. 13.4 - Prob. 34ECh. 13.4 - Prob. 35ECh. 13.4 - Prob. 36ECh. 13.4 - Prob. 37ECh. 13.4 - Prob. 38ECh. 13.4 - Prob. 39ECh. 13.4 - Prob. 40ECh. 13.4 - Prob. 41ECh. 13.4 - Prob. 42ECh. 13.4 - Prob. 43ECh. 13.5 - A large company decided to donate 17 computers to...Ch. 13.5 - Prob. 2TTOCh. 13.5 - Prob. 3TTOCh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - What is the quota rule? Which apportionment...Ch. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - The table shows the enrollment at two campuses of...Ch. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Write an essay explaining why many people feel...Ch. 13 - Use this information for Exercises 14: the...Ch. 13 - Use this information for Exercises 14: the...Ch. 13 - Use this information for Exercises 14: the...Ch. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Use this information for Exercises 917: a large...Ch. 13 - Prob. 16RECh. 13 - Use this information for Exercises 917: a large...Ch. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Prob. 23RECh. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - A community college bought 15 laptop computers to...Ch. 13 - Prob. 31RECh. 13 - Prob. 32RECh. 13 - Prob. 33RECh. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Repeat exercise 30 using the Huntington-Hill...Ch. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Prob. 40RECh. 13 - Prob. 41RECh. 13 - Prob. 42RECh. 13 - Prob. 43RECh. 13 - Prob. 1CTCh. 13 - Prob. 2CTCh. 13 - Prob. 3CTCh. 13 - Prob. 4CTCh. 13 - Prob. 5CTCh. 13 - Prob. 6CTCh. 13 - Prob. 7CTCh. 13 - Prob. 8CTCh. 13 - Use this information for Exercises 512: a small...Ch. 13 - Prob. 10CTCh. 13 - Prob. 11CTCh. 13 - Prob. 12CTCh. 13 - Prob. 13CTCh. 13 - An airline offers nonstop flights from Fort...Ch. 13 - Prob. 15CTCh. 13 - Repeat Problem 14 using Websters method.Ch. 13 - Repeat Problem 14 using the Huntington-Hill...Ch. 13 - Prob. 18CTCh. 13 - Prob. 19CTCh. 13 - Prob. 20CTCh. 13 - Prob. 21CT
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- Consider the weighted voting system [11: 7, 4, 1]Find the Shapley-Shubik power distribution of this weighted voting system.List the power for each player as a fraction: P1: P2: P3:arrow_forwardConsider the weighted voting system [18: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction: P1: P2: P3: P4:arrow_forwardConsider the weighted voting system [16: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction: P1: P2: P3: P4:arrow_forward
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