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Question: 2 points 5 4 4 0 6 dominic annie florence...

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(2 points) 5 4 4 0 6 Dominic Annie Florence Dominic Florence Annie Annie Dominic Florence Annie Florence Dominic Florence Dominic Annie Florence Annie Dominic Construct an example with 19 voters in which: 1) Dominic would win with the Plurality method 2) Annie would win with the Borda count method and be a Condorcet candidate (and win with Pairwise Comparison as well), 3) Florence would win if Plurality with Elimination is used 4) Also, Annie has a total of two first place votes. To do this, you will need to answer Parts (a)-(e) so you can fill in the numbers at the top of the preference schedule (a) We have seen that last place votes can make it difficult for someone to win with some of the voting methods. Which of the three candidates should not get any last place votes? Annie (b) Which two columns have the candidate you chose in part (a) in last place (at the bottom)? Select all columns where the candidate you chose in part (a) is in last place. There is more than one correct answer - pick them both. A. Column 1 B. Column 2 C. Column 3 D. Column 4 E. Column 5 F Column 6 Once you get Parts (a) and (b) correct, you now know two columns that should have zeroes at the top of them in the preference schedule to represent no ballots of those orderings from the voters. (c) Florence must win with Plurality with Elimination, but notice that Florence cannot be a majority candidate, because Dominic is supposed to have the most first place votes. If Florence has over 50%, then Dominic must also have more than that, which would be over 50%, and it is not possible for two people to both have over 50% of the first place votes. Hence someone would get eliminated if Plurality with Elimination is usedWhich candidate would get eliminated during Plurality with Elimination? Look at the number of votes that one of the candidates is supposed to get in Clue 4. Could this candidate have the fewest first place votes? Annie (d) There are two columns where the candidate you found in Part (c) is in first place. When this candidate is eliminated, each column with give new first place votes to one of the other two candidates. Since we want Florence to win with Plurality with Elimination, we want to choose a column where your candidate from Part (c) is in first, and Florence is positioned to get new first place votes after this candidate is eliminated Look at the columns where the candidate you chose in part (c) is in first place. Which one will also give first place votes to Florence when this candidate is eliminated? (PICK ONE) A. Column 1 B. Column 2 C. Column 3 D. Column 4 E. Column 5 Column 6 The column you chose in Part (d) will then have all of the first place votes for the candidate you found in Part (c) The other column that has the candidate you found in Part (c) in first place will give first place votes to someone other than Florence. We do not want that, so we should put a zero above this column At this point, you should have numbers above both columns where the candidate from Part (c) is in first place (e) Now there are only two columns left. They each have a different candidate at the top of them. Let us work on Dominic. Dominic must have the most first place votes, but we do not want to make Dominic a majority candidate. Otherwise, Dominic would automatically win with Plurality with Elimination, and Florence would lose. We need to give Dominic enough first place votes to have the most, but not over 50% What is the minimum number of first place votes needed to be a majority candidate in this election? 10 Once you get Part (e) correct, you now know that Dominic should have fewer first place votes than your answer to Part (e). How much fewer? Well Dominic should still start with the most first place votes. You should be able to figure out how many first place votes Dominic must have, and then you can have the remaining voters (who have not given first place votes to Dominic or Annie) in the remaining column where Florence is at the top.

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