6. a. Explain what the majority criterion states. b. In problem #2, which candidate did you determine to be the winner using the Borda count method? Has the majority criterion been violated? Why or why not? Explain clearly by stating in complete sentences. c. In a school election, there were 3 candidates: Aiden, Kyle and Brandon. The preference table is given below. Number of voters 18 17 K A A B KA 1st Choice 2ND Choice 3rd Choice 21 28 K B B The winner of this election using the Borda count is Aiden (work is not shown for this). Has the majority criterion been violated? Why or why not? Explain clearly by stating your answer in complete sentences. 7. a. Explain what the monotonicity criterion states. b. Consider an election between Xu, Smith and Unger. The preference table is given below. The winner using the plurality-with-elimination method is Smith. Show work to verify this 26 22 Number of voters 20 14 X S U 1st Choice 2ND Choice 3rd Choice AKB XUS UKS XASN U S X c. Now suppose the first election was declared invalid due to suspicion of voting machine error. When a second election was held, everyone voted the same, except the 20 voters in the first column decided to change their vote to favor Smith (the winner of the original election using plurality-with-elimination method). They changed their ballot to S.X and then U. Did the reelection violate the monotonicity criterion? Why or why not? Explain clearly by showing work and stating your answer in complete sentences.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Transcribed Image Text:1/outline/file/44889344 1 O 6. a. Explain what the majority criterion states. b. In problem #2, which candidate did you determine to be the winner using the Borda count method? Has the majority criterion been violated? Why or why not? Explain clearly by stating in complete sentences. c. In a school election, there were 3 candidates: Aiden, Kyle and Brandon. The preference table is given below. Number of voters 18 17 21 28 K A K A A В' B K B K A B 1st Choice 2ND Choice 3rd Choice The winner of this election using the Borda count is Aiden (work is not shown for this). Has the majority criterion been violated? Why or why not? Explain clearly by stating your answer in complete sentences. 7. a. Explain what the monotonicity criterion states. b. Consider an election between Xu, Smith and Unger. The preference table is given below. The winner using the plurality-with-elimination method is Smith. Show work to verify this 100 Number of voters 1st Choice 2ND Choice 3rd Choice suspicion of voting machine error. When a second c. Now suppose the first election was declared invalid due election was held, everyone voted the same, except the 20 voters in the first column decided to change their vote to favor Smith (the winner of the original election using plurality-with-elimination method). They changed their ballot to S, X, and then U. Did the reelection violate the monotonicity criterion? Why or why not? Explain clearly by showing work and stating your answer in complete sentences. 8. a. Explain what the irrelevant criterion requires. b. A class is choosing among 4 candidates for president: Matthews (M), Bradford (B), Green (G), and Chad (C). The preference table is shown below. 20 14 26 22 X X U S U X U S U S S X Number of voters 17 16 8 2 B G C G C M D 1 Choice 2ND Choice New tab - Profile 1... H M C DELL O File - Google Chro...

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