1.2. Consider the following two-candidate profile: AABAAABBBBBBBBBAB B Who wins under: (a) the simple majority method? (b) the 2/3 super-majority method? (c) the parity method? (d) the weighted voting system where the first 6 voters get 3 votes, the next 6 voters get 2 votes, and the rest get 1?

1.2. Consider the following two-candidate profile: AABAAABBBBBBBBBAB B Who wins under: (a) the simple majority method? (b) the 2/3 super-majority method? (c) the parity method? (d) the weighted voting system where the first 6 voters get 3 votes, the next 6 voters get 2 votes, and the rest get 1?

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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F959 - QUESTION 4. BORDA COUNT. The animals get sick and tired of having the Lion be the King of the Jungle, and they overthrow the Lion and hold an election for President of the Jungle. The candidates an the Zebra, the Elephant, the Baboon and the Hyena, and there are 67 voters. The 67 preference lists fall into 6 categories, as summarized below. Using the Borda count method, show the results of the election. 15 Zebra 13 Baboon 12 Zebra 10 Elephant Elephant Hyena 4₂15760 4•13=524.12 48 4.10€ 40 4x936 4×8=33 Hyena Hyena Baboon Hyena Elephant 3-15-45 3-13-39 3·12-30 3·10-30 3x9-27) 3x 8-24 Baboon Zebra Baboon Elephant 1.13 €13/1•12= 12 1·10 = (10) 9 Baboon Zebra Hyena Elephant Elephant Zebra 215- (30) 2.13 (24) 2-12 (24) 2·10 -(20) 2×9=182x8=16) Baboon Zebra 1.15-(15 Hyena 8 1x9 ✓9-9 1x8=8
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In the upcoming election between two close candidates, a poll reports that Jonesleads Smith. For each of the following situations, how confident are you thatJones will win?a) Jones leads with 51% preference with a margin of error of +or-3%.b) Jones leads with 52% preference with a margin of error of +or-3%.c) Jones leads with 54% preference with a margin of error of +or-3%.
2. Given the following weighted voting system [78: 24, 40, 14], is there a dictator? If so, which player?
Discuss the following problems as a cooperative effort. Seventeen people serve on a board and are considering three alternatives: A, B, and C. Here are the choices followed by vote: (ABC) = 8 (ACB) = 4 (BAC) = 3 (BCA) = 0 (CAB) = 2 (CBA) = 5 Determine the winner, if any, using the voting methods in Problems A-G. D. Majority rule E. Plurality method F. Borda Count method G. Hare Method
3. Given the following weighted voting system [16: 12, 7, 4], is there a player that has the veto power? If so, which player and why? Write your response below:
Consider the weighted voting system {25: 26, 11, 7, 4, 3}. Are there any players that are dictators, or players with veto power, or dummy players? If so, identify who the players are. a Dictator(s) = Player 1, Veto Power = Player 2, Dummy Player(s) = Player 2, 3, 4, 5 b Dictator(s) = Player 1, Veto Power = nobody, Dummy Player(s) = 1, 2, 3, 4, 5 Dictator(s) = Player 1, Veto Power = Player 1, Dummy Player(s) = Player 1, 2, 3, 4, 5 %3D %3D d. Dictator(s) = Player 1, Veto Power = Player 1, Dummy Player(s) = Player 2, 3, 4, 5 %3D %3D O O O O
Problem: Setting the Beatles aside, one hundred people were asked to rank their preferences for the greatest rock group between four choices, using 1 for their favorite and 4 for their least favorite. The results are shown in the table below. (Attached picture) Which candidate would be the favorite using 1) The Plurality voting method? 2) The Plurality with Elimination voting method?
Consider the weighted voting system [q: 13, 11, 10, 8, 4]. Assume that this system has no dictators and is not subject to gridlock. (a) What is the weight of the coalition formed by P,, P3, and P? (b) For what values of the quota q is the coalition formed by P,, Pa, and P, a winning coalition? (c) For what values of the quota q is the coalition formed by P,, P3, and Pa a losing coalition? (a) What is the weight of the coalition formed by P2, Pa, and P? The weight of the coalition (P2, P3, Pa) is. (b) For what values of the quota q is the coalition formed by P2, P3, and Pa a winning coalition? The coalition {P2, P3, Pa) is a winning coalition for all values of q from through . (c) For what values of the quota q is the coalition formed by P,, Pa, and P a losing coalition? The coalition {P2, P3, Pa) is a losing coalition for all values of q from through . MacBook Air F2 G00 F4 FS F9 @ #3 2$ % * 3 4 8 9. Q Y A S D K V alt option command comm ర N
Use Plurality Runoff to determine the winner of the following election: Number of Voters (13) 3 2 C D A B D E First Second Third Fourth Fifth 4 A B C D E 3 B A с D E B C A E 1 E D C B A Now, use this election to show that Plurality Runoff FAILS to satisfy Monotonicity. By this, we mean to move the winning candidate to a higher position on one of the preference lists so that the candidate no longer wins.