Mergers. Sometimes in a weighted voting system two or more players decide to merge-that is to say, to combine their votes and always vote the same way. (Note that a merger is different from a coalition-coalitions are temporary, whereas mergers are permanent.) For example, if in the weighted voting system
a. Consider the weighted voting system
b. Consider the weighted voting system
c. Rework the problem in (b) for the weighted voting system
d. What are your conclusions from (a), (b), and (c)?
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MYMATHLAB ACCESS F/MGF 1107
- Refer to the weighted voting system [27: 15, 10, 8, 4]. The Banzhaf power distribution of the weighted voting system is: P1 : ["", "", "", ""] P2 : ["", "", "", ""] P3 : ["", "", "", ""] P4 : ["", "", "", ""]arrow_forwardConsider the weighted voting system 25:18,14,w_(3). What is the largest possible value for the weight w_(3) which guarantees P_(3) is the only player who is a dummy?arrow_forwardFor a weighted voting system {q: 8, 3, 3, 2} with q an interger and 9 is less than or equal to q, which is less than or equal to 16, how do you determine for the values of q where there is a dummy?arrow_forward
- A weighted voting system for voters A, B, C, D, and E is given by { 35: 29, 11, 8, 4, 2 }. The weight of voter A is 29, the weight of voter B is 11, the weight of voter C is 8, the weight of voter D is 4, and the weight of voter E is 2. Determine the (A) WINNING COALITIONS and for each winning coalitions determine the (B) CRITICAL VOTERarrow_forwardConsider the weighted voting system [q: 9, 5, 1].Which values of q result in a dictator (list all possible values)What is the smallest value for q that results in exactly one player with veto power who is not a dictator?What is the smallest value for q that results in exactly two players with veto power?arrow_forwardA telecommunication company proposed construction of a cell site tower in a certain city. To determine whether this is to be constructed, a vote is to be taken among the residents of a city and the surrounding barangays. Many residents in the barangays feel that the proposal will pass because of the large proportion of city voters who favor the construction. A poll is taken to determine if there is a significant difference in the proportion of city voters and barangay voters favoring the proposal. If 250 of 400 city voters favor the proposal and 360 of 500 barangay residents favor it, would you agree that the proportion of city voters favoring the proposal is higher than the proportion of barangay voters? Use a 0.025 level of significance.arrow_forward
- 2. A fraternity votes to choose a service project--visiting nursing homes, reading with children in elementary schools, or cleaning up a stretch of highway. Their preference rankings are as follows: Number of Voters 3 1 4 8 2 Visiting nursing homes 1 1 2 3 2 Reading with children 2 3 1 1 3 Cleaning highway 3 2 3 2 1 Is there a Condorcet winner? If there is no Condorcet winner, is there a Weak Condorcet winner? Show the work you do in deciding, including vote totals, and state your conclusion.arrow_forward5. A vote is to be taken among the residents of a town and the surrounding county to determine whether a proposed chemical plant should be constructed. The construction site is within the town limits, and for this reason many voters in the county believe that the proposal will pass because of the large proportion of town voters who favor the construction. To determine if there is a significant difference in the proportions of town voters and county voters favoring the proposal, a poll is taken. If 120 of 200 town voters favor the proposal and 240 of 500 county residents favor it, would you agree that the proportion of town voters favoring the proposal is higher than the proportion of county voters? Use an α = 0.05 level of significance.arrow_forwardFor the weighted voting system [24: 21, 21, 5], which of the following is a true statement? Group of answer choices The system has a dictator. The system has a player with veto power. The system has a dummy. None of the above statements is true.arrow_forward
- Use the Banzhaf power index to determine the power index for each player. Consider the voting system {43: 30, 25, 20, 10}. Find each player’s power index. a P1 = 40%, P2 = 30%, P3 = 30%, P4 = 0% b P1 = 30%, P2 = 30%, P3 = 40%, P4 = 0% c P1 = 30%, P2 = 40%, P3 = 30%, P4 = 0% d P1 = 35%, P2 = 30%, P3 = 35%, P4 = 0%arrow_forwardConsider the weighted voting system [15: 9, 6, 3, 1] and the Banzhaf Power distribution method, which player(s) are critical in the coalition { P1, P2, P3}? Group of answer choices P1 P2 P1 and P2 P1, P2 and P3arrow_forwardConsider the weighted voting system [15: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction:P1P1: P2P2: P3P3: P4P4:arrow_forward
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