(a) Explanation Given: The video game choices are sport (S), action (A) and role-playing (R). The election results to decide what type of video game play by the three candidate is listed below in table. Number of votes 10 6 5 First choice R S S Second choice A R A Third choice S A R Calculation: The winner using the pair-wise comparisons method, first need to make three pair-wise comparisons R vs A, R vs S and A vs S. First, compare R vs A: Number of votes 10 6 5 First choice R S S Second choice A R A Third choice S A R From the above table, the Game R is ranked higher than A with 10 + 6 = 16 ballots (columns 1, and 2) and candidate A is also ranked higher than R with 5 ballots (column 3). Thus, the game R rewarded 1 point because R gets 16 ballots which is greater than A ballots (b) To determine To compare: The winner with the one determined by the Borda count method.

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Author: sobecki

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Chapter 12.3, Problem 16E

(a)

To determine

The winner using the pair-wise comparison voting method.

(b)

To determine

To compare: The winner with the one determined by the Borda count method.

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Chapter 12.3, Problem 15E

Chapter 12.3, Problem 17E

Chapter 12 Solutions

MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS

Ch. 12.1 - The Student Activities Committee at Camden College...Ch. 12.1 - An election was held for the chairperson of the...Ch. 12.1 - Prob. 3TTO Ch. 12.1 - Prob. 4TTO Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Explain the head-to head comparison criterion.Ch. 12.1 - 5. What is a fairness criterion for an election? Ch. 12.1 - Prob. 6E

Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - For Exercises 15–18, rewrite the preference table...Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Using the election results given in Exercise 9,...Ch. 12.1 - 20. Using the election results given in Exercise...Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Using the Internet as a resource, look up the...Ch. 12.1 - Suppose that an election has seven candidates, and...Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prob. 27E Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.2 - Prob. 1TTO Ch. 12.2 - Prob. 2TTO Ch. 12.2 - Prob. 3TTO Ch. 12.2 - If the one voter who listed softball last in the...Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Can a candidate that gets the least first-place...Ch. 12.2 - A gaming club holds a vote to decide what type of...Ch. 12.2 - The McKees Point Yacht Club Board of Directors...Ch. 12.2 - Prob. 9E Ch. 12.2 - A local police union is holding an election for a...Ch. 12.2 - Students at a college were asked to rank three...Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Does the election in Exercise 12 violate the...Ch. 12.2 - An English department is voting for a new...Ch. 12.2 - The Association of Self-Employed Working Persons...Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Suppose that all 4 voters from the last column of...Ch. 12.2 - Suppose that 2 of the 4 voters from the second...Ch. 12.2 - If 2 of the voters from column 1 in Exercise 21...Ch. 12.2 - If the 3 voters in column 4 in Exercise 22 change...Ch. 12.2 - Construct a preference table for an election...Ch. 12.2 - Construct a preference table for an election...Ch. 12.2 - Construct a preference table for an election so...Ch. 12.2 - If the candidates on a preference ballot are...Ch. 12.2 - If the candidates on a preference ballot are...Ch. 12.2 - In an election with four candidates, how many...Ch. 12.2 - Based on your answers to Exercise 32, explain why...Ch. 12.2 - One way to avoid the issue described in Exercises...Ch. 12.2 - Lets talk about a modified Borda count method....Ch. 12.3 - Prob. 1TTO Ch. 12.3 - Prob. 2TTO Ch. 12.3 - Does the election in Try This One 2 violate the...Ch. 12.3 - Prob. 4TTO Ch. 12.3 - Explain how to determine the winner of an election...Ch. 12.3 - Prob. 2E Ch. 12.3 - Describe Arrows impossibility theorem. How is it...Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Which of the five voting methods we studied do you...Ch. 12.3 - If all of the voters in an approval voting...Ch. 12.3 - Fill in the table below, which summarizes our five...Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - Prob. 12E Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - The McKees Point Yacht Club Board of Directors...Ch. 12.3 - The students in Dr. Lees math class are asked to...Ch. 12.3 - If Professor Donovan was unable to serve as...Ch. 12.3 - If the travel company from Exercise 14 loses its...Ch. 12.3 - If the West Oak Golf Club is unavailable and the...Ch. 12.3 - If a room for Dr. Lees final exam was not...Ch. 12.3 - A sports committee of students needs to choose a...Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.3 - Prob. 27E Ch. 12.3 - Prob. 28E Ch. 12.3 - Prob. 29E Ch. 12.3 - Construct a preference table so that one candidate...Ch. 12.3 - Prob. 31E Ch. 12.3 - Prob. 32E Ch. 12.3 - Prob. 33E Ch. 12.3 - Evaluate each voting method we studied if there...Ch. 12.3 - Suppose that in an election for city council,...Ch. 12.3 - Prob. 36E Ch. 12.3 - Devise a method for breaking ties when using...Ch. 12.3 - Prob. 38E Ch. 12.4 - Prob. 1TTO Ch. 12.4 - Prob. 2TTO Ch. 12.4 - Prob. 3TTO Ch. 12.4 - Prob. 4TTO Ch. 12.4 - Prob. 5TTO Ch. 12.4 - Assign the 30 seats from Try This One 5 using...Ch. 12.4 - Prob. 7TTO Ch. 12.4 - Prob. 8TTO Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Describe how to find the upper and lower quotas...Ch. 12.4 - Prob. 5E Ch. 12.4 - Prob. 6E Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - In Exercises 912, find the standard divisor for...Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Prob. 16E Ch. 12.4 - Prob. 17E Ch. 12.4 - Prob. 18E Ch. 12.4 - Prob. 19E Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Prob. 24E Ch. 12.4 - Prob. 25E Ch. 12.4 - For Exercises 2628 find: (a)The standard divisor....Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - Prob. 33E Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.4 - Prob. 38E Ch. 12.4 - Prob. 39E Ch. 12.4 - Prob. 40E Ch. 12.4 - Prob. 41E Ch. 12.4 - Prob. 42E Ch. 12.4 - Prob. 43E Ch. 12.5 - Prob. 1TTO Ch. 12.5 - Try This One 2 A county with three districts has...Ch. 12.5 - Prob. 3TTO Ch. 12.5 - Prob. 1E Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - Prob. 4E Ch. 12.5 - What is the quota rule? Which apportionment...Ch. 12.5 - Prob. 6E Ch. 12.5 - Prob. 7E Ch. 12.5 - Prob. 8E Ch. 12.5 - Prob. 9E Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - The table shows the enrollment at two campuses of...Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Write an essay explaining why many people feel...Ch. 12.5 - 18. Which do you think is more serious: violating...Ch. 12 - Use this information for Exercises 14: the...Ch. 12 - Use this information for Exercises 14: the...Ch. 12 - Use this information for Exercises 14: the...Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Use this information for Exercises 917: a large...Ch. 12 - Prob. 16RE Ch. 12 - Use this information for Exercises 917: a large...Ch. 12 - Prob. 18RE Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Prob. 27RE Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - A community college bought 15 laptop computers to...Ch. 12 - Prob. 31RE Ch. 12 - Prob. 32RE Ch. 12 - Prob. 33RE Ch. 12 - Prob. 34RE Ch. 12 - Prob. 35RE Ch. 12 - Repeat exercise 30 using the Huntington-Hill...Ch. 12 - Prob. 37RE Ch. 12 - Prob. 38RE Ch. 12 - Prob. 39RE Ch. 12 - Prob. 40RE Ch. 12 - Prob. 41RE Ch. 12 - Prob. 42RE Ch. 12 - Prob. 43RE Ch. 12 - Prob. 1CT Ch. 12 - Prob. 2CT Ch. 12 - Prob. 3CT Ch. 12 - Prob. 4CT Ch. 12 - Prob. 5CT Ch. 12 - Prob. 6CT Ch. 12 - Prob. 7CT Ch. 12 - Prob. 8CT Ch. 12 - Use this information for Exercises 512: a small...Ch. 12 - Prob. 10CT Ch. 12 - Prob. 11CT Ch. 12 - Prob. 12CT Ch. 12 - Prob. 13CT Ch. 12 - An airline offers nonstop flights from Fort...Ch. 12 - Prob. 15CT Ch. 12 - Repeat Problem 14 using Websters method.Ch. 12 - Repeat Problem 14 using the Huntington-Hill...Ch. 12 - Prob. 18CT Ch. 12 - Prob. 19CT Ch. 12 - Prob. 20CT Ch. 12 - Prob. 21CT

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The winner using the pair-wise comparison voting method.

Solution Summary: The author analyzes the election results to determine the winner using the pair-wise comparison voting method.

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The winner using the pair-wise comparison voting method.

To compare: The winner with the one determined by the Borda count method.

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Chapter 12 Solutions