2. Given the following weighted voting system [78: 24, 40, 14], is there a dictator? If so,which player?

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Answered: 2. Given the following weighted voting…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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5. In a recent electrion, 72% of the voters voted to elect candidate Lopez for mayor. In the same election, 60% of the voters voted in favor of Proposition Q. 54% of the voters voted for both candidate Lopez and also voted in favor of Proposition Q. Find the propability that a randomly selected voter... a. ... voted for Lopez OR voted in favor of Proposition Q. b. ... voted for Lopez, given that they voted in favor of Proposition Q. c. ... didn't vote for Lopez nor did they vote for in favor of Proposition Q.
13. Copeland's rule is a voting system that, like Condorcet's method, looks at one-on-one contests. It, however, takes as the election winner the candidate with the best "win-loss record." Use the following ballots to show that Copeland's rule is manipulable: Election 1 a. Who is the winner of Election 1? Number of voters (4) first A A D second third fourth В fifth OBECA D OBA
For the weighted voting system [12: 8,6,5,3]: a. List all coalitions; identify which are winning coalitions. b. Determine the critical players in each winning coalition. Determine the Banzhaf power distribution for the system. C.
2 30 Each family in Green Country is classified as living in an urban, rural, or suburban location. During a given year, 15% of all urban families move to a suburban location, and 5% move to a rural location; also, 6% of all suburban families move to an urban location, and 4% move to a rural location; finally, 4% of all rural families move to an urban location, and 6% move to a suburban location. a. If a family now lives in an urban location, what is the probability that it will live in an urban area two years from now? A suburban area? A rural area? b. Suppose that at present, 40% of all families live in an urban area, 35% live in a suburban area, and 25% live in a rural area. Two years from now, what percentage of Green Country families will live in an urban area? c. What is the future population distribution of the Green Country at the steady state?
Thirty-eight cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. Of these cities, 19 had a professional sports team, 18 had a symphony, 20 had a children's museum, 13 had a professional sports team and a symphony, 11 had a professional sports team and a children's museum, 11 had a symphony and a children's museum, and 7 had all three activities. How many cities have a pro sports team or a symphony but not a childrens museum?
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:
2. A new location for a park in a small city outside of Bucklin, Colorado, is going to be built. The citizens get to vote on 1 of 4 locations: • Century, • Midland, • Uber, • Southern. The voting population is 6800 citizens. Votes 1st 2nd 3rd 4th 2150 Century Midland Southern Uber 1150 Midland Uber Southern Century 1100 Uber Southern Midland Century 1600 Southern Century Uber Midland a. The location that has the most first place votes is b. The location that has the fewest first place votes is c. The location we eliminate is d. Fill in the new table. Votes 1st 2nd 3rd 4th 2150 1150 1100 1600 e. Is there a majority of votes for a location now? Yes or no? f. Which location if any should get eliminated now? g. Fill in the new table. Votes 1st 2nd 3rd 2150 1150 1100 1600 h. Is there a majority of votes for a location now? If yes, what is that location, and how many the first place votes does that location have? i. What location won the plurality vote or single location voting method?…
5. Divide and conquer. You're again facing your friend, Brenda, in a "candy-off” game involving a pile of 100 caramels and the winner's prize: one peppermint patty. (Like before, you still LOVE peppermint patties!). On their turn, each player can remove a
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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
4. Consider the weighted voting system [14: 14, 10, 2, 1]. a. What is the quota? b. How many players are there? c. Identify any dictators. d. Identify any players with veto power. e. Identify any dummy player.
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

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2. Given the following weighted voting system [78: 24, 40, 14], is there a dictator? If so, which player?