1. Consider the following preference ballots for candidates A, B, C, and D:Number of votersRankings 654 21st choice AD2nd choice BBD3rd choice DCB4th choice C A AUDсBUDCAFor each of the voting systems we have studied (plurality/first-past-the-post, two-round sys-tem, Borda count, and instant run-off/ranked choice voting), determine who would win theelection.

The objective of this question is to determine the winner of an election under four different voting…

Answered: 1. Consider the following preference…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following election. Number of Voters 16 11 12 4 1st Choice B D A B 2nd Choice A A D D 3rd Choice D B C C 4th Choice C C B A Using the Plurality Method, the winner of the election is Group of answer choices C D A B
An organization with branches across the Northeast is trying to decide where it should hold its annual employee picnic. Each branch ranks the locations of Augusta, ME; Boston, MA; and Erie, PA, and the following preference schedule is created: Number of Votes 36 24 19 16 13 1st Choice Erie Augusta Boston Augusta Boston 2nd Choice Augusta Erie Erie Boston Augusta 3rd Choice Boston Boston Augusta Erie Erie The organization has chosen to use the Borda Count method to determine which city they will hold their picnic in. Where will the organization’s picnic be held? Make sure to include an explanation along with your answer.
Select one of the following awards for this discussion: Academy Award for Best Picture Grammy Award for Best Album Heisman Trophy Nobel Peace Prize Pulitzer Price for Fiction For the award you selected, answer the following four questions: How are the nominees selected? Who votes? What type of voting is used? Remember the methods we studied in this unit - majority, plurality, plurality with elimination, Borda count method, Pairwise comparison method. Is one of these types of voting methods used or another method? Describe the method used. Who tabulates the results?
1. Thirteen members of a dinner committee want to decide what kind of background music will be played during a meal. Their choices are easy listening, jazz, classical, and new age. Following are their preference rankings: Number of Voters Easy Listening 1 3 1 2 2 2 1 1 1 1 1 2 2 3 4 4 Jazz 3 3 1 1 3 Classical 3 2 4 4 1 1 2 New age 4 4 4 3 3 4 1 A) What option would win using the plurality method? (Show vote totals) B) top two finishers? (Show vote totals) What option would win using the plurality method with a runoff between the C) counts. (You should say if you are using Easy Borda method). Which candidate would win using the Borda method? Show the Borda
A group of college students was surveyed to determine their favorite class among History, Mathematics, and Art. The students ranked the classes in order of preference, and the results are shown below. (a) Using plurality voting, which class is the students' favorite? (b) Did that class recieve a majority vote? Rankings History 1 1 2 2 3 3 Mathematics 2 3 1 3 1 2 Art 3 2 3 1 2 1 Number of Students: 25 37 16 34 19 35 (a) History (b) No (a) Art (b) No (a) Math (b) No (a) History (b) Yes (a) Art (b) Yes
Consider the preference schedule (below) for an election. (a) Determine the winner using the plurality method. (b) Determine the winner using sequential runoff. First D A B C B Second C B A D C Third A C C A D Fourth B D D B A Votes 31 26 22 15 8
Mr. Abdul Rheman's class held an election for class president. Instead of just voting for one candidate, students need to rank all the candidates according to their preference. The results are shown below: Rankings 2 1 2 3 1 Y 2 1 2 3 1 3 1 3 1 2 2 Number of 8 7 7 8 6. 7 Students Number of Votes for the Winner by Plurality.
For an election with four candidates (A, B, C, D) consider the following preference table: NUMBER OF 6 3 5 8 VOTERS 1st Choice D D A C 2nd Choice В A C 3rd Choice A В В D |4th Choice C C D B Using the majority method, which candidate wins the election? ОА ов No winner
2. Suppose that an employer decides to hire a new CEO using the Borda count. A panel of 35 managers, board members, and other executives rank the candidates using a preference ballot. Here is the preference schedule. 1st Place Chen Ashford Ashford 2nd Place Ashford Borge Chen 3rd Place Borge Chen Borge Voters 18 16 1 (a) Find the Borda count for each of the candidates to determine who will be hired. (b) Now forget the Borda counts and look at the number of first place votes. (c) Does any candidate have a majority of the votes? Which one? (d) Does Criterion 1 apply? Has Criterion 1 been satisfied? (e) Again, forget the Borda counts and look at the number of first place votes in pairwise comparisons. Who wins in a race between Chen and Ashford? between Chen and Borge? (f) Is there a Condorcet winner? Did the Condorcet winner win the election? (g) Does Criterion 2 apply? Has Criterion 2 been satisfied?

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