MATHEMATICAL EXCURSIONS>LL<
4th Edition
ISBN: 9780357097977
Author: Aufmann
Publisher: CENGAGE LEARNING (CUSTOM)
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 4.2, Problem 1ES
To determine
What is the difference between a majority and a plurality? Is it possible to have one without the other?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Ques 46, 47 and 48 are three subparts.
The students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small
majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are
some yellow supporters who would actually vote for red. The results of the vote are below.
Blue
Yellow
Red
46%
44%
10%
What statement below is correct about adding a third choice to the plurality vote?
O a
Ob
Oc
d
Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of
students preferred yellow over blue when there were two choices.
Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though
a majority of students preferred yellow over blue when there were two choices.
Red did not win the vote, so because of this, yellow should win the vote over blue.…
Politician Paul and Candidate Carl are running for governor, and the election is next week. The latest poll shows that Politician Paul has 46% of the vote, while Candidate Carl has 43% of the vote. The news report, however, states that this poll contains a 3% margin of error.
a) What does this mean for Politician Paul?
b) What does this mean for Candidate Carl?
c) What do these poll results tell you about the upcoming election?
Chapter 4 Solutions
MATHEMATICAL EXCURSIONS>LL<
Ch. 4.1 - Verify this apportionment using the Jefferson...Ch. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Prob. 3EECh. 4.1 - Find the apportionment that would have resulted if...Ch. 4.1 - Explain how to calculate the standard divisor of...Ch. 4.1 - Teacher Aides A total of 25 teacher aides are to...Ch. 4.1 - In the Hamilton apportionment method, explain how...Ch. 4.1 - Prob. 4ESCh. 4.1 - Governing Boards The following table shows how the...Ch. 4.1 - Forest Rangers The table below shows how the...
Ch. 4.1 - Sales Associates The table below shows the number...Ch. 4.1 - Hospital Interns The table below shows the number...Ch. 4.1 - House of Representatives The U.S. House of...Ch. 4.1 - College Enrollment The following table shows the...Ch. 4.1 - Medical Care A hospital district consists of six...Ch. 4.1 - What is the Alabama paradox?Ch. 4.1 - What is the population paradox?Ch. 4.1 - What is the new states paradox?Ch. 4.1 - 15. What is the Balinski-Young Impossibility...Ch. 4.1 - Apportionment of Projectors Consider the...Ch. 4.1 - Hotel Management A company operates four resorts....Ch. 4.1 - Prob. 18ESCh. 4.1 - Management Scientific Research Corporation has...Ch. 4.1 - Prob. 20ESCh. 4.1 - Elementary School Teachers The following table...Ch. 4.1 - Social Workers The following table shows the...Ch. 4.1 - Computer Usage The table below shows the number of...Ch. 4.1 - The population of Illinois increased by over...Ch. 4.1 - Prob. 25ESCh. 4.1 - Prob. 26ESCh. 4.1 - Computer Usage Use the Webster method to apportion...Ch. 4.1 - Demographics The table below shows the populations...Ch. 4.1 - Which of she following apportionment methods can...Ch. 4.1 - According to Michael Balinski and H. Peyton Young,...Ch. 4.1 - 31. What method is presently used to apportion the...Ch. 4.1 - Prob. 32ESCh. 4.1 - John Quincy Adams, the sixth president of the...Ch. 4.1 - In the Huntington-Hill method of apportionment,...Ch. 4.1 - Prob. 35ESCh. 4.2 - Using the Borda method of voting, which flavor of...Ch. 4.2 - Instead of using the normal Borda method, suppose...Ch. 4.2 - Prob. 3EECh. 4.2 - Suppose the Borda method used in Exercise I of...Ch. 4.2 - Prob. 5EECh. 4.2 - Can the assignment of points for first. Second,...Ch. 4.2 - Prob. 7EECh. 4.2 - Prob. 1ESCh. 4.2 - Explain why the plurality voting system may not be...Ch. 4.2 - Prob. 3ESCh. 4.2 - Explain how the plurality with elimination voting...Ch. 4.2 - Prob. 5ESCh. 4.2 - Prob. 6ESCh. 4.2 - Is there a best voting method? Is one method more...Ch. 4.2 - Explain why. if only two candidates are running,...Ch. 4.2 - Presidential Election The table below shows the...Ch. 4.2 - Breakfast Cereal Sixteen people were asked to rank...Ch. 4.2 - Cartoon Characters A kindergarten class was...Ch. 4.2 - Catering A 15-person committee is having lunch...Ch. 4.2 - Movies Fifty consumers were surveyed about their...Ch. 4.2 - Breakfast Cereal Use the Borda count method of...Ch. 4.2 - Prob. 15ESCh. 4.2 - Catering Use the Borda count method of voting to...Ch. 4.2 - Class Election A senior high school class held an...Ch. 4.2 - Cell Phone Usage A journalist reviewing various...Ch. 4.2 - Baseball Uniforms A Little League baseball team...Ch. 4.2 - Radio Stations A number of college students were...Ch. 4.2 - Class Election Use plurality with elimination to...Ch. 4.2 - Prob. 22ESCh. 4.2 - Campus Club A campus club has money left over in...Ch. 4.2 - Recreation A company is planning its annual summer...Ch. 4.2 - X-Men Movies Fans of the X-Men movies have been...Ch. 4.2 - Prob. 26ESCh. 4.2 - School Mascot A new college needs to pick a moscot...Ch. 4.2 - Election Five candidates are running for president...Ch. 4.2 - Prob. 29ESCh. 4.2 - Radio Stations Use the pairwise comparison method...Ch. 4.2 - Does the winner in Exercise tic satisfy the...Ch. 4.2 - 32. Does the winner in Exercise 12 satisfy the...Ch. 4.2 - Prob. 33ESCh. 4.2 - Prob. 34ESCh. 4.2 - Prob. 35ESCh. 4.2 - Prob. 36ESCh. 4.2 - Election Three candidates are running for mayor. A...Ch. 4.2 - Film Competition Three films have been selected as...Ch. 4.2 - 39. Election A campus club needs to elect four...Ch. 4.2 - Scholarship Awards The members of a scholarship...Ch. 4.2 - Another method of voting is to assign a weight. or...Ch. 4.2 - Prob. 42ESCh. 4.2 - Prob. 43ESCh. 4.3 - Using the data in Example 1 on page 211, list all...Ch. 4.3 - For the data in Example I on page 211, calculate...Ch. 4.3 - Prob. 3EECh. 4.3 - Prob. 4EECh. 4.3 - Create a voting system with three members that is...Ch. 4.3 - Prob. 6EECh. 4.3 - Prob. 7EECh. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - In the following exercises that involve weighted...Ch. 4.3 - Prob. 3ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 8ESCh. 4.3 - Prob. 9ESCh. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Calculate, if possible, the l3anzhaf power index...Ch. 4.3 - Prob. 13ESCh. 4.3 - Prob. 14ESCh. 4.3 - Music Education A music department Consists of a...Ch. 4.3 - Prob. 16ESCh. 4.3 - Criminal Justice In a criminal trial, each of the...Ch. 4.3 - Criminal Justice In California civil court cases,...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Identify any dictator and all dummies for each...Ch. 4.3 - Prob. 21ESCh. 4.3 - Prob. 22ESCh. 4.3 - Football At the beginning of each football season,...Ch. 4.3 - Prob. 24ESCh. 4.3 - Prob. 25ESCh. 4.3 - Prob. 26ESCh. 4.3 - Consider the weighted voting system { q:8,3,3,2 },...Ch. 4.3 - Prob. 28ESCh. 4.3 - Prob. 29ESCh. 4.3 - UN Security Council The United Nations C Security...Ch. 4 - Education The following table shows the...Ch. 4 - Airline Industry The following table shows the...Ch. 4 - Airline Industry The table below shows how the...Ch. 4 - 4. Education The following table shows the number...Ch. 4 - Technology A company has four offices. The...Ch. 4 - Automobile Sales Consider the apportionment of 27...Ch. 4 - Music Company MusicGalore.biz has offices in Los...Ch. 4 - Building Inspectors A city apportions 34 building...Ch. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Corporate Security The Huntington-Hill...Ch. 4 - Essay Contest Four finalists are competing in an...Ch. 4 - Ski Club A campus ski club is trying o decide...Ch. 4 - Prob. 14RECh. 4 - Consumer Preferences A group of consumers were...Ch. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Homecoming Queen Three high school students are...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - A weighted voting system for voters A. B. C. D....Ch. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - 25. Calculate the Banzhaf power indices for voters...Ch. 4 - Calculate the Banzhaf power indices for voters A,...Ch. 4 - Prob. 27RECh. 4 - Identify any dictator and all dummies for each...Ch. 4 - Four voters. A. B. C. and D. make decisions by...Ch. 4 - Postal Service The table below shows the number of...Ch. 4 - Computer Allocation The following table shows the...Ch. 4 - High School Counselors The following table shows...Ch. 4 - Prob. 4TCh. 4 - Consumer Preference One hundred consumers ranked...Ch. 4 - Prob. 6TCh. 4 - Exam Review A professor is preparing an extra...Ch. 4 - Prob. 8TCh. 4 - Drama Department The four staff members. A, B,C,...Ch. 4 - Three voters. A. B. and C, make decisions by using...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?arrow_forwardConsider an election with 301 voters cast for 3 candidates. What is the smallest number of first-place votes that a candidate can receive to win by the Plurality method?arrow_forwardA radio talk show host with a large listening audience is interested in the proportion p of adults in his listening area that think that the United States should not be at war in Afghanistan. He asks this question to his listeners "Do you think the United States should be at war in Afghanistan?" He asks his listeners to phone in and vote "yes" if they agree that the United States should be at war in Afghanistan and "no" if they disagree. Of the 100 people who phoned in 85% answered "yes". Which of the following assumptions for inference about a proportion using a confidence interval was violated? Select one: 1. The data are a simple random sample from the population of interest. 2.There appear to be no violations. 3. The sample size "n" is so large that both the count of successes n * p and the count of failures n(1-p) are 10 or more 4.The population is at least 10 times as large as the sample.arrow_forward
- Answer the following questions for the voter profile shown to the right. Number of Voters Ranking 17 a >b>c> d >e (a) Which alternative is a majority candidate? (b) Which alternative is the Borda method winner? (c) Does the Borda method violate the majority criterion for the voter profile? 4 b>c>d>e > a 3 c>d>b> e>a 4 d>b>c> a >e 3. e >c>d> a > b (a) Which alternative is a majority candidate? e a There is no majority candidate. (b) Which alternative is the Borda method winner? e a b. O There is no Bordamethod winner. (c) Does the Borda method violate the majority criterion for the voter profile? Yes No O Time Remaining: 01:53:38 Next E O O O @ O 0 oarrow_forwardA public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas. They randomly select 50 voters from each county in the state and ask whether they approve or disapprove of the measure.This is an example ofarrow_forwardA telecommunication company proposed construction of a cell site tower in a certain city. To determine whether this is to be constructed, a vote is to be taken among the residents of a city and the surrounding barangays. Many residents in the barangays feel that the proposal will pass because of the large proportion of city voters who favor the construction. A poll is taken to determine if there is a significant difference in the proportion of city voters and barangay voters favoring the proposal. If 250 of 400 city voters favor the proposal and 360 of 500 barangay residents favor it, would you agree that the proportion of city voters favoring the proposal is higher than the proportion of barangay voters? Use a 0.025 level of significance.arrow_forward
- In a three candidate race that is decided using the plurality method what is the fewest votes that the winner could get if there were 40 votes cast? Explain.arrow_forwardTwo counties are going to be polled about their support for a proposed ballot initiative. 2,000 people have been polled in the first county, which has a population size of 200,000. Other things being equal (such as the actual support for the ballot initiative in each county), how many people do we need to poll in the second county to achieve a similar level of accuracy, if the second county has a population of 2 million people? Group of answer choices 2,000 people 20,000 people 200,000 people No answer text providedarrow_forwardUsing the plurality-with-elimination method, who wins the election if candidate E is removed from the ballot?arrow_forward
- A Senior High School class held an election for class president. Instead of just voting for one candidate, the students needed to rank all the candidates according to preference. The table presents the results. RANKINGS Anton 2 3 1 3 4 2 Maria 4 1 3 4 1 3 Shelly 1 2 2 2 3 4 Troy 3 4 4 1 2 1 Number of Votes 36 53 41 27 31 45 1. Who is the winner by plurality? 2. What is the majority number of votes?arrow_forwardA county clerk wants to improve voter registration. He wants to send out reminders in the mail to all citizens in the county who are eligible to vote. To determine if it will actually improve voter registration, a random sample of 1250 potential voters was taken. No reminders were sent out to a group of 625 eligible voters and of those 625, 299 registered to vote. Reminders were sent out to another group of 625 voters and of those 348 registered to vote. The county clerk claims that the proportion of people who registered was significantly greater in the group that was sent the reminders. Using a 0.10 significance level, test the claim that the proportion of registered voters is higher in the group that received the reminders. What is the test statistic for this test? A county clerk wants to improve voter registration. He wants to send out reminders in the mail to all citizens in the county who are eligible to vote. To determine if it will actually improve voter registration, a…arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Grade 12 and UG/ Introduction to logical statements and truth tables; Author: Dr Trefor Bazett;https://www.youtube.com/watch?v=q2eyZZK-OIk;License: Standard YouTube License, CC-BY