Consider the weighted voting system [18: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction: P1: P2: P3: P4:
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Consider the weighted voting system [18: 15, 8, 3, 1]
Find the Banzhaf power distribution of this weighted voting system.
List the power for each player as a fraction:
P1:
P2:
P3:
P4:
Step by step
Solved in 2 steps
- Use the Banzhaf power index to determine the power index for each player. Consider the voting system {18: 9, 6, 3, 3, 2}. Use the winning coalitions below to find each player’s power index. {P1, P2, P3} {P1, P2, P4} {P1, P2, P3, P4} {P1, P2, P3, P5} {P1, P2, P4, P5} {P1, P2, P3, P4, P5} a P1 = 33.3%, P2 = 33.3%, P3 = 11.1%, P4 = 11.1%, P5=0% b P1 = 37.5%, P2 = 31.5%, P3 = 11.1%, P4 = 11.1%, P5 = 8.8% c P1 = 33.3%, P2 = 33.3%, P3 = 11.1%, P4 = 11.1%, P5 = 3% d P1 = 33.5%, P2 = 37.5%, P3 = 11.1%, P4 = 11.1%, P5 = 6.8%Consider the weighted voting system [16: 15, 8, 3, 1]Find the Banzhaf power distribution of this weighted voting system.List the power for each player as a fraction: P1: P2: P3: P4:The students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are some yellow supporters who would actually vote for red. The results of the vote are below. Blue Yellow Red 46% 44% 10% What statement below is correct about adding a third choice to the plurality vote? O a Ob Oc d Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, so because of this, yellow should win the vote over blue.…
- Use the Banzhaf power index to determine the power index for each player. Consider the voting system (58: 40, 35, 25, 16). Find each player's power index. a b с d P1 = 33.3%, P2 = 33.3%, P3 = 0%, P4 = 33.3% P1 = 33.3%, P2 = 33.3%, P3 = 33.3%, P4 = 0% P1 = 33.3%, P2 = 30%, P3 = 36.7%, P4 = 0% P1 = 36.7%, P2 = 37.5%, P3 = 33.3%, P4 = 0%Use the Banzhaf power index to determine the power index for each player. Consider the voting system (16: 7, 6, 3, 3, 2). Use the winning coalitions below to find each player's power index. • {P1, P2, P3} • {P1, P2, P4) • • {P1, P2, P3, P4} {P1, P2, P3, P5} {P1, P2, P4, P5} • {P1, P2, P3, P4, P5} a b с d P1 = 37.5%, P2 = 35.5%, P3 = 12.5%, P4 = 12.5%, P5 = 2% P1 = 37.5%, P2 = 37.5%, P3= 10.5%, P4 = 12.5%, P5 = 0% P1 = 40%, P2 = 34%, P3= 12.5%, P4 = 12.5%, P5 = 0% P1 = 37.5%, P2 = 37.5%, P3= 12.5%, P4 = 12.5%, P5 = 0%Consider the weighted voting system [9: 7, 4, 1]Find the Shapley-Shubik power distribution of this weighted voting system.List the power for each player as a fraction:P1: P2: P3:
- Consider the weighted voting system[32: 10,6,6,5,4,4,3,2,1]Find:The total number of players: The total number of votes: The quota:see photo, please.Riverside Elementary school is holding a school-wide election to choose a school color. FIve-Eighths of the votes were blue, 5/9 of the remaining votes were for green, and the remaining 48 votes were red. how many votes were blue? How many votes were for green?
- Suppose that three candidates-Woodward, Seiple, and Porter-are running in an election that will be decided by the plurality method with a runoff between the top two finishers if none of the candidates receives a majority of the votes. The results of the first ballot (plurality) are given next. Woodward 2315 Seiple Porter 1885 800 In a runoff election between Woodward and Seiple, what is the smallest percentage of Porter supporters that would need to vote for Seiple in order for Seiple to win the election?Mr. Abdul Rheman's class held an election for class president. Instead of just voting for one candidate, students need to rank all the candidates according to their preference. The results are shown below: Rankings X 3 2 1 3 1 Y 2 2 1 3 1 3 1 2 Number of 8 7 8 6 7 Students If you will use Borda Count Method, wherein the assigned points for 1st, 2nd and 3rd place are 3pts, 2pt, and 1pt respectively, who will be the class president of Mr. Abdul Rheman and by how much points?Use the Borda method to determine the winner of the election for the school president. There are 4 candidates. They are A, B, C, and D. The school’s clubs voted for the president. They ranked their choices and below is the result. Clubs 1 3 4 Number of Votes 40 25 30 18 First A B C D Second B A D В Third C D Fourth D C A A 1. Assign the poi values to each vote. Fill in the table below. Clubs 1 2 3 4 Number of Votes 40 25 30 18 First (4 pts) A В D Second (3 pts) A D Third (2 pts) D Fourth (1 pt) D C A A 2. Calculate the total points for each candidate. Show how you calculate each candidate's total points. А: В: С: D: 3. Under the Borda method, the winner is