The Mathematics Department is holdingan election for department chair. Eachmember ranks the candidates from firstto third. The preference table belowshows the results of the ballots withcandidates Clark (C), Jones (J), andSmith (S).Number of Votes 7 10 4 8FirstSecondThirdJSJ CSJC SCCS JDetermine the winner using the Bordacount method. Did the winner receive amajority of the first place votes using theBorda count method?Select one:a. Smith; NoO b.Smith; YesO c. Jones; Nod.Clark; Yese.Jones; YesO f. Clark; No

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Answered: The Mathematics Department is holding…

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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The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). Number of Votes 7 10 4 8 First JS JC Second S JCS Third CCS J After some discussion and quibbling from the committee about each candidate, a second election is then held resulting in the following preference table. The Mathematics Department is holding an election for department chair. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Clark (C), Jones (J), and Smith (S). Number of Votes 7 11 First Second Third CCS J If the plurality with elimination method is used to determine the winner, is the monotonicity criterion satisfied? Select one: a. No b. Yes 3 8 JSJC S JCS
Consider the following election. This is the same table as above. 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 with the Elimination Method, the winner of the election is Group of answer choices D C B A
Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The chart below shows the preference schedule. Voter 1 1st choice A 2nd choice B 3rd choice C 4th choice D Voter 2 B C D A Voter 3 C B D A Voter 4 D B C A Voter 5 A D C B 6. With the previous example, what is the outcome if you use the Borda count method?
110 voters are asked to rank four brands of cereal: A, B, C, and D. The votes are summarized in the preference table shown below. Determine the winner using the plurality-with-elimination method. Number of Votes First Choice Second Choice Third Choice Fourth Choice 42 35 20 13 В A A B A A В В D O o o C
7)
Solve the problem. 6) A condominium association is holding an election for president of the board of directors. Each member ranks the candidates from first to third. The preference table below shows the results of the ballots with candidates Abbott (A), Blake (B), Cleary (C), and Downs (D). Number of Votes 3 6 5 8 7 4 6 6 4 First ABAACBDC C Second CABCDDBBA B C C DAA ADD DDDB B CCAB Third Fourth If the plurality method if used to determine the winner and Downs drops out, is the irrelevant alternatives criterion satisfied?
A team is planning a group vacation to one of the following locations: Alaska (A), Florida (F), San Antonio (S), or Hawaii (H). The employees rank the four possible sites according to the following preference table: No. of 5 7 7 5 6. 8 Votes 1st A F A A H F 2nd 3rd A 4th F A H F A If the locations are arranged according to the length of travel, the fastest to reach will be San Francisco, followed by Alaska, then Florida, and last will be Hawaii. If we will use Sequential Pairwise Voting, which location will be chosen? (A) Alaska в) Hawai Florida D) San Francisco
Ten voters are asked to rank 4 brands of cell phones: A, B, C, and D. The ten voters turn in the following ballots showing their preferences in order A B B BA B B B BA AB BCA C с DACA CD D D D D D C D D Second Which of the following preference tables correctly shows the results of the voting? Select one: O a. Number of Votes 2 2 First A B Third Fourth A C в BACA CCAD D Second O b. Number of Votes 2 2 First A B A Third D C 1 B A D C 1 B A D A 1 B с D A B C Fourth D D C O c. None of these is correct. d. Number of Votes 2 2 First D 2 A 2 C C 2 3 B C A D 3 B с A D 3 B D с C
A football team needs to select a captain from among four players-Steel, Griffin, Pollard, and Driggs. The preference rankings for the team are as follows: # of votes 12 5 8 1 10 3 2 Steel 1 1 2 4 2 2 Griffin 2 3 1 1 1 4 4 Pollard 3 2 3 4 2 1 3 Driggs 4 4 4 2 3 3 1 A) What are the vote totals using the Plurality method? B) Who would win using Plurality with a Runoff between the top two finishers? (Show both vote totals)

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