Explanation The winner of the election using the plurality method is as follows. The first-place votes for each candidates are X: 3, Y: 2 and X: 1. Here, the candidate X gets most number of first place votes and declared as the winner of the election. Thus, X wins the election by plurality method. Obtain the winner of the election using the Borda count method. Borda count method is a procedure to choose the winner in an election. Each candidate is ranked from the most favorable to least favorable such that 1 point is given to the last place candidate, 2 points to the second last place candidate and so on. The candidate with the highest points is declared as the winner of the election. For the choice X, the points are calculated as follows, The 3 First-place votes produce 3 ⋅ 3 = 9 points, 2 + 1 = 3 Second-place votes produce 3 ⋅ 2 = 6 points and 0 Third-place votes produce 0 ⋅ 1 = 0 point. Thus, the total points for X are 9 + 6 + 0 = 15 points. For the choice Y, the points are calculated. The 2 First-place votes produce 2 ⋅ 3 = 6 points, 0 Second-place votes produce 0 ⋅ 2 = 0 points and 3 + 1 = 4 Third-place votes produce 4 ⋅ 1 = 4 point. Hence, the total points for Y are 6 + 4 = 10 points. For the choice Z, the points are calculated. The 1 First-place votes produce 1 ⋅ 3 = 3 points, the 3 Second-place votes produce 3 ⋅ 2 = 6 points and 2 Third-place votes produce 2 ⋅ 1 = 2 points. Thus, the total points for Z are 6 + 3 + 2 = 11 points. Here, X acquires more points. Therefore, X wins with Borda count method. Obtain the winner of the election by plurality-with-elimination method: Plurality with elimination method involves a procedure to choose a candidate as a winner who receives majority of first place votes

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Chapter 12.3, Problem 29E

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To construct: A preference table with three candidates X, Y and Z so that the same candidates wins the election using all of the plurality, Borda count, plurality-with-elimination and pairwise comparison methods.

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Chapter 12.3, Problem 28E

Chapter 12.3, Problem 30E

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Chapter 12 Solutions

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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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To construct: A preference table with three candidates X, Y and Z so that the same candidates wins the election using all of the plurality, Borda count, plurality-with-elimination and pairwise comparison methods.

Solution Summary: The author explains how to construct a preference table with three candidates X, Y and Z so that the same candidates wins the election using all of the plurality, Borda count and pairwise comparison methods.

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To construct: A preference table with three candidates X, Y and Z so that the same candidates wins the election using all of the plurality, Borda count, plurality-with-elimination and pairwise comparison methods.

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Chapter 12 Solutions