The preference table for an election is given below. Using the Borda count method, Dwas declared the winner.Number of Votes1 Cholce2nd Cholce3 Choice4th Choice5020100CBAACCBIs the majority criterion satished?O No, the candidate who received the majority of first-place votes lost the election.O No, the winner of the election recelved the majority of votesO Yes, the candidate who received the majority of first-place votes won the electionO Yes, the candidate who recelved the majority of first-place votes lost the election.8BDAC Suppose that the modified divisor that Jefferson chose did not work There are 32 seats to apportion and his first try gave him a total of35. What would be his next step?O Try a larger modified divisor to decrease the number of seats.O Forget about It and watch some TVO Try a smaller modified divisor to decrease the number of seatsO Call Adams for help.

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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 J S J C Second S J C S Third C C S J If the Borda count method is used to determine the winner, is the majority criterion satisfied? No Yes
In a recent survey, people were asked to vote for their favorite films of all time. The five movies were A, B, C, D, and E. Consider the hypothetical results below. Number of Votes First Choice Second Choice Third Choice Forth Choice Fifth Choice 17 15 9 A C D C 21 A B C B E CEE D B D A B E D A Apply the following different voting methods to identify the winner: (i) plurality method, (ii) Borda Count method, (iii) plurality-with-elimination, and (iv) pairwise comparison method.
O K Before a conference, a panel of participants voted on the topic for the keynote address. The choices were (G)lobal Warming, (E)conomy, (F)oreign Policy, (P)overty, and (T)echnology. The votes are summarized in the preference table shown at right. What topic is selected using the plurality-with-elimination method? Select the winner below. O Technology 000 Global Warming Poverty Foreign Policy O Economy Number of Votes 1st 2nd 3rd 4th 5th 15 G E F co -Twat oo 3PTEEG CHEL F E P 13 5 2 E F P T P T T P G F E G G
8
Use the plurality with elimination method to determine the winner and compare it to the plurality method. Who wins the preferential vote and the single candidate vote? There are 74 voters and the candidates need 37 votes to win. There are 5 candidates for the house of representatives and you have to rank them by preference. Votes 20 16 12 15 11 1st Emilio Howard Richard Melissa Hannah 2nd Howard Melissa Hannah Hannah Emilio 3rd Melissa Emilio Melissa Richard Richard 4th Hannah Richard Emilio Howard Howard 5th Richard Hannah Howard Emilio Melissa a Plurality with elimination: Richard wins with 43, Plurality: Emilio wins with 20 Plurality with elimination: Melissa wins with 43, Plurality: Emilio wins with 20 Plurality with elimination: Hannah wins with 43, Plurality: Emilio wins with 20 d. Plurality with elimination: Emilio wins with 37, Plurality: Emilio wins with 20
6
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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?
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 Second Third JSJ C SJC S CCS J Determine the winner using the Borda count method. Did the winner receive a majority of the first place votes using the Borda count method? Select one: a. Smith; No O b. Smith; Yes O c. Jones; No d. Clark; Yes e. Jones; Yes O f. Clark; No
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
Four candidates, Harrison (H), Lennon (L), McCartney (M), and Starr (S), are running for regional manager. After the polls close, ranked ballots are tallied, and the results are summarized in the table. Use the plurality method of voting to determine the winner. Harrison Lennon McCartney Starr Number of Ballots Cast 45 95 24 91 30 13 18 1st choice H L L M M S S 2nd choice L M S L L H M 3rd choice S H M H S L H 4th choice M S H S H M L
There is a reunion of 25 years being held for old classmates. The large group is trying to pick who will play at the reunion for them. Their options are Reo (R), Boston (B), Journey (J), and Fleet (F). 1. Who is picked if Borda Count is used? 2. Who gets picked if Pairwise comparison is used? 3. If plurality method is used, who gets picked?

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