Mathematics All Around (6th Edition)
6th Edition
ISBN: 9780134434681
Author: Tom Pirnot
Publisher: PEARSON
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Chapter 11.2, Problem 33E
To determine
To make:
A preference table with the given conditions.
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In an election with three candidates, A, B, and C, the voters have the following preferences: 12% approve of A only. 19% approve of A (first choice) but also approve of B. 17% approve of B (first choice) but also approve of A. 25% approve of C (first choice) but also approve of A. 27% approve of C (first choice) but also approve of B. a. Which candidate wins an approval vote? b. Fairness Criterion 1 states, “If a candidate receives a majority of the first-place votes, that candidate should be the winner.” Is this criterion satisfied in this election? Explain.
According to a student survey on keyboard light preference, 44% liked white, 26% liked blue and 30% liked green. 8% liked both white and green, 12% liked both white and blue, 10% liked both green and blue. If 84% of them liked at least one keyboard light color, what percentage of people liked all three?
brandon conducted a research to determine the preference of students during online classes. From the 250 students who participated in the study, 85 wanted to have synchronous classes, 90 wanted to have asynchronous classes, and 100 wanted to have blended learning. From the respondents, it was seen that 35 preferred either synchronous and asynchronous, 10 preferred synchronous and blended learning, 25 preferred blended learning and asynchronous, and exactly 55 liked two of the mode of learning.
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Chapter 11 Solutions
Mathematics All Around (6th Edition)
Ch. 11.1 - Four candidates running for a vacant seat on the...Ch. 11.1 - Five candidates running for mayor receive votes as...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The university administration has asked a group of...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...Ch. 11.1 - The drama society members are voting for the type...
Ch. 11.1 - Before a conference on Trends in the next Decade,...Ch. 11.1 - Before a conference on Trends in the next Decade,...Ch. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - A small employee-owned Internet company is voting...Ch. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - A small employee-owned Internet company is voting...Ch. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - In Exercises 23-26, refer to the preference table...Ch. 11.1 - Prob. 24ECh. 11.1 - In Exercises 23-26, refer to the preference table...Ch. 11.1 - Prob. 26ECh. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - In Exercises 27-30, refer to the preference table...Ch. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Math in Your Life: Between the Numbers Instant...Ch. 11.1 - In approval voting, a person can vote for more...Ch. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.2 - Some of these exercises have no fixed solution...Ch. 11.2 - Some of these exercises have no fixed solution...Ch. 11.2 - Determining the legal drinking age. A state...Ch. 11.2 - Voting for the president of a club. A chapter of...Ch. 11.2 - Choosing a location for a research facility. Teach...Ch. 11.2 - Locating a new factory. The Land Mover Tractor...Ch. 11.2 - Reducing a budget. Due to a decrease in state...Ch. 11.2 - Voting on an award for best restaurant. A group of...Ch. 11.2 - Use the following preference table for Exercises 9...Ch. 11.2 - Use the following preference table for Exercises 9...Ch. 11.2 - Complete the preference table so that the Borda...Ch. 11.2 - Complete the preference table so that A is the...Ch. 11.2 - Prob. 13ECh. 11.2 - Make a preference table similar to the one given...Ch. 11.2 - Complete the preference table so that the...Ch. 11.2 - Does the plurality method satisfy the majority...Ch. 11.2 - Does the plurality-with-elimination method satisfy...Ch. 11.2 - Prob. 18ECh. 11.2 - Presidential election. One of the several...Ch. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - A run off election. Repeat Exercise 21 using this...Ch. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Voters are choosing among five options. Make a...Ch. 11.2 - Make a preference table, similar to the one given...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - One of the voting methods we have been discussing...Ch. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - In Exercises 1-12, the weight represent voters A,...Ch. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - In Exercises 13-16, write out all winning...Ch. 11.3 - Prob. 14ECh. 11.3 - In Exercises 13-16, write out all winning...Ch. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - In Exercises 29-34, determine the Banzhaf power...Ch. 11.3 - Prob. 34ECh. 11.3 - The system [3:1,1,1,1,1] is an example of a one...Ch. 11.3 - Prob. 36ECh. 11.3 - Consider the system [14:15,2,3,3,5] in which A is...Ch. 11.3 - Prob. 38ECh. 11.3 - Calculating power in the electoral college. After...Ch. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - In Example 5, we analyzed the voting power of the...Ch. 11.3 - In Example 5, we analyzed the voting power of the...Ch. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - A dummy in a weighted voting system is a voter...Ch. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - In Exercises 55 and 56, devise a voting system...Ch. 11.3 - Prob. 56ECh. 11.4 - In Exercises 1 4, use tree diagrams to find all...Ch. 11.4 - Prob. 2ECh. 11.4 - In Exercises 1 4, use tree diagrams to find all...Ch. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - In Exercises 1116, determine the Shapley-Shubik...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - The system [3:1,1,1,1,1] is an example of a one...Ch. 11.4 - Measuring power on a jury. We can consider a...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Measuring power on a theater guild. The Theater...Ch. 11.4 - Measuring power on a state committee. The college...Ch. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - A new social media company, Chirp, has an...Ch. 11.4 - Prob. 27ECh. 11.4 - Measuring power among states. Repeat Exercise 27...Ch. 11.4 - Explain the difference between the Banzhaf index...Ch. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CT - Prob. 1CTCh. 11.CT - Prob. 2CTCh. 11.CT - Prob. 3CTCh. 11.CT - Prob. 4CTCh. 11.CT - Prob. 5CTCh. 11.CT - Prob. 6CTCh. 11.CT - Prob. 7CTCh. 11.CT - Prob. 8CTCh. 11.CT - Prob. 9CTCh. 11.CT - Determine the Banzhaf power index for each voter...Ch. 11.CT - Prob. 11CTCh. 11.CT - Prob. 12CTCh. 11.CT - Prob. 13CTCh. 11.CT - Prob. 14CTCh. 11.CT - Prob. 15CTCh. 11.CT - Prob. 16CT
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- To assess the likely results of an upcoming election, the 5 members of a presumably representative "focus group" of eligible voters are each asked to rank the 3 candidates, A, B, and C, in the order of their preference (1=most preferred, 3=least preferred). The investigator wants to determine if there is a difference between candidates with respect to the preference of the subjects. The table below shows the results. Member A B C 1 2 3 1 2 1 2 3 3 1 3 2 4 3 1 2 5 1 3 2 State the hypotheses. What statistical test should be used to determine if there is a difference between candidates with respect to the preference of the subjects? Determine the appropriate critical value and set up the decision rule. (α=0.01) Compute the test statistic. Interpret your results. Give your conclusion.arrow_forward2. A fraternity votes to choose a service project--visiting nursing homes, reading with children in elementary schools, or cleaning up a stretch of highway. Their preference rankings are as follows: Number of Voters 3 1 4 8 2 Visiting nursing homes 1 1 2 3 2 Reading with children 2 3 1 1 3 Cleaning highway 3 2 3 2 1 Is there a Condorcet winner? If there is no Condorcet winner, is there a Weak Condorcet winner? Show the work you do in deciding, including vote totals, and state your conclusion.arrow_forwardA researcher would like to determine the political preference of the nationbefore the upcoming midterm elections. From where should the researchercollect his/her data? A. From all the voting population in the nation.B. From a sample of people living in one region.C. From a sample of people randomly chosen across the nation.D. From all the people in a randomly selected region.arrow_forward
- Qw.17.arrow_forwardIn a recent survey, Gallup asked a sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Partial results for the individuals who expressed a preference, broken down by gender, are displayed in the two-way table. Job Outside Stay at Total of the Home Home Male 391 ??? 504 Female 254 219 473 Total 645 332 977 What proportion of respondents would prefer a job outside of the home? Round your answer to two decimal places. i 0.34arrow_forwardA company studies the product preferences of 20,000 consumers. It was found that each of the products A, B and C was liked by 7500, 6500 and 5500 respectively and all the products were liked by 1230. Products A and B were liked by 2500, products A and C were liked by 2300 and products B and C were liked by 2530. Prove that the study results are not correct.arrow_forward
- . The principal at Eisenstein Elementary School has just retired. The school board must hire a new princi- pal amongst the candidates Mrs. Anderson, Mr. Borda, Ms. Chapman, and Mr. Donald. After interview- ing the 4 finalists, each of the 11 school board members ranks the candidates. The preference schedule is below. a. 6 1st Choice A B 3 C C D D B A 28 2nd Choice B 3rd Choice с 4th Choice D Determine the plurality winner. Did that candidate receive the majority? A b. Determine the Condorcet winner. C. Determine the Borda count winner.arrow_forwardA charity is trying to raise money by hosting a comedy club with a famous comedian. In order to maximize donations they want to bring in the best comedian, if there is one. By surveying 100 of their target donors, they find the following preferences: Comedian Zach Galifianakis Maria Bamford Patton Oswalt Brian Posehn Number of Preferences 11 44 23 22 They are trying to determine who (if anyone) should be invited. Calculate the test statistic for one of the tests. What is the correct decision to make? (Do not reject H0, Reject H0, Nothing can be concluded, or None of the above?) What is the correct action to take? Invite Zach Galifianakis, Invite Maria Bamford, Invite Patton Oswalt, Invite Brian Posehn, Invite none of these, or None of the other options are correct)arrow_forwardplease explain !arrow_forward
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