Explanation Given: The choices in the restaurant are lemon-crusted salmon (L), crab-stuffed chicken (C), garlic prime rib (G) and wasabi rolls (W). The results of the competition listed below in following preference table. Number of Votes 8 6 5 3 2 First choices C L W G W Second choices W W G C C Third choices G G C W L Fourth choice L C L L G Calculation: Winner of the election using the plurality method: Form the preference table, the first place vote for each candidates C, L, W and G. The first place-votes for C is 8 votes. Similarly, the first-place votes for L is 6 votes. The first-place votes for W is 5 + 2 = 7 and the first-place votes for G is 3. Since, the Crab-stuffed chicken (C) received the most of 8 first-place plurality votes; thus, Crab-stuffed chicken (C), wins the election. The winner of the election using the head-to-head comparison method: The idea is to compare all combinations of two candidates at a time to see which is preferred in a head-to-head matchup without the third candidate involved. First compare W with L: Column Candidate preferred over other candidates Voters Head-to-Head comparison 1 2 3 4 5 W L L W W L W L W L 8 6 5 3 2 W win over L Hence, W was preferred over L by 8 + 5 + 3 + 2 = 18 votes; L was preferred over W by 6 votes, meaning in a head-to-head comparison, W wins over L. Next, compare G with L: Column Candidate preferred over other candidates Voters Head-to-Head comparison 1 2 3 4 5 G L L G G L G L L G 8 6 5 3 2 G win over L Hence, G was preferred over L by 8 + 5 + 3 = 16 votes; L was preferred over G by 6 + 2 = 8 votes, meaning in a head-to-head comparison, G wins over L. Next, compare C with L: Column Candidate preferred over other candidates Voters Head-to-Head comparison 1 2 3 4 5 C L L C C L C L C L 8 6 5 3 2 C win over L Hence, C was preferred over L by 8 + 5 + 3 + 2 = 18 votes; L was preferred over C by 6 votes, meaning in a head-to-head comparison, C wins over L

Connect Math hosted by ALEKS Access Card 52 Weeks for Math in Our World

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ISBN: 9781259232848

Author: David Sobecki, Allan Bluman

Publisher: McGraw-Hill Education

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Chapter 13.1, Problem 14E

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To explain: Whether the head-to-head comparisons criterion violate the results in Exercise 10.

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Chapter 13.1, Problem 13E

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Connect Math hosted by ALEKS Access Card 52 Weeks for 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. 3TTO Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Explain the head-to head comparison criterion.Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E

Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - Using the election results given in Exercise 9,...Ch. 13.1 - Prob. 14E Ch. 13.1 - Prob. 15E Ch. 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. 19E Ch. 13.1 - Prob. 20E Ch. 13.1 - Prob. 21E Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Prob. 24E Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.2 - Prob. 1TTO Ch. 13.2 - Prob. 2TTO Ch. 13.2 - Prob. 3TTO Ch. 13.2 - If the one voter who listed softball last in the...Ch. 13.2 - Prob. 1E Ch. 13.2 - Prob. 2E Ch. 13.2 - Prob. 3E Ch. 13.2 - Prob. 4E Ch. 13.2 - Prob. 5E Ch. 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. 9E Ch. 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. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 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. 21E Ch. 13.2 - Prob. 22E Ch. 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. 1TTO Ch. 13.3 - Prob. 2TTO Ch. 13.3 - Does the election in Try This One 2 violate the...Ch. 13.3 - Prob. 4TTO Ch. 13.3 - Explain how to determine the winner of an election...Ch. 13.3 - Prob. 2E Ch. 13.3 - Describe Arrows impossibility theorem. How is it...Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 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. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - Prob. 13E Ch. 13.3 - Prob. 14E Ch. 13.3 - Prob. 15E Ch. 13.3 - Prob. 16E Ch. 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. 24E Ch. 13.3 - Prob. 25E Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - Prob. 29E Ch. 13.3 - Construct a preference table so that one candidate...Ch. 13.3 - Prob. 31E Ch. 13.3 - Prob. 32E Ch. 13.3 - Prob. 33E Ch. 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. 36E Ch. 13.3 - Devise a method for breaking ties when using...Ch. 13.3 - Prob. 38E Ch. 13.4 - Prob. 1TTO Ch. 13.4 - Prob. 2TTO Ch. 13.4 - Prob. 3TTO Ch. 13.4 - Prob. 4TTO Ch. 13.4 - Prob. 5TTO Ch. 13.4 - Assign the 30 seats from Try This One 5 using...Ch. 13.4 - Prob. 7TTO Ch. 13.4 - Prob. 8TTO Ch. 13.4 - Prob. 1E Ch. 13.4 - Prob. 2E Ch. 13.4 - Prob. 3E Ch. 13.4 - Describe how to find the upper and lower quotas...Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - Prob. 7E Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - In Exercises 912, find the standard divisor for...Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Prob. 17E Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - Prob. 21E Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - For Exercises 2628 find: (a)The standard divisor....Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - Prob. 30E Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - Prob. 34E Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E Ch. 13.4 - Prob. 39E Ch. 13.4 - Prob. 40E Ch. 13.4 - Prob. 41E Ch. 13.4 - Prob. 42E Ch. 13.4 - Prob. 43E Ch. 13.5 - A large company decided to donate 17 computers to...Ch. 13.5 - Prob. 2TTO Ch. 13.5 - Prob. 3TTO Ch. 13.5 - Prob. 1E Ch. 13.5 - Prob. 2E Ch. 13.5 - Prob. 3E Ch. 13.5 - Prob. 4E Ch. 13.5 - What is the quota rule? Which apportionment...Ch. 13.5 - Prob. 6E Ch. 13.5 - Prob. 7E Ch. 13.5 - Prob. 8E Ch. 13.5 - Prob. 9E Ch. 13.5 - Prob. 10E Ch. 13.5 - Prob. 11E Ch. 13.5 - Prob. 12E Ch. 13.5 - The table shows the enrollment at two campuses of...Ch. 13.5 - Prob. 14E Ch. 13.5 - Prob. 15E Ch. 13.5 - Prob. 16E Ch. 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. 4RE Ch. 13 - Prob. 5RE Ch. 13 - Prob. 6RE Ch. 13 - Prob. 7RE Ch. 13 - Prob. 8RE Ch. 13 - Prob. 9RE Ch. 13 - Prob. 10RE Ch. 13 - Prob. 11RE Ch. 13 - Prob. 12RE Ch. 13 - Prob. 13RE Ch. 13 - Prob. 14RE Ch. 13 - Use this information for Exercises 917: a large...Ch. 13 - Prob. 16RE Ch. 13 - Use this information for Exercises 917: a large...Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Prob. 22RE Ch. 13 - Prob. 23RE Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - A community college bought 15 laptop computers to...Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - Prob. 35RE Ch. 13 - Repeat exercise 30 using the Huntington-Hill...Ch. 13 - Prob. 37RE Ch. 13 - Prob. 38RE Ch. 13 - Prob. 39RE Ch. 13 - Prob. 40RE Ch. 13 - Prob. 41RE Ch. 13 - Prob. 42RE Ch. 13 - Prob. 43RE Ch. 13 - Prob. 1CT Ch. 13 - Prob. 2CT Ch. 13 - Prob. 3CT Ch. 13 - Prob. 4CT Ch. 13 - Prob. 5CT Ch. 13 - Prob. 6CT Ch. 13 - Prob. 7CT Ch. 13 - Prob. 8CT Ch. 13 - Use this information for Exercises 512: a small...Ch. 13 - Prob. 10CT Ch. 13 - Prob. 11CT Ch. 13 - Prob. 12CT Ch. 13 - Prob. 13CT Ch. 13 - An airline offers nonstop flights from Fort...Ch. 13 - Prob. 15CT Ch. 13 - Repeat Problem 14 using Websters method.Ch. 13 - Repeat Problem 14 using the Huntington-Hill...Ch. 13 - Prob. 18CT Ch. 13 - Prob. 19CT Ch. 13 - Prob. 20CT Ch. 13 - Prob. 21CT

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Whether the head-to-head comparisons criterion violate the results in Exercise 10.

Solution Summary: The author explains that the head-to-head comparisons criterion violated because W won over all other candidates C, G, and L.

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To explain: Whether the head-to-head comparisons criterion violate the results in Exercise 10.

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Chapter 13 Solutions