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 (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 {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%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%
- What method of voting is described below?Voters rank options or candidates in order of preference. Each candidate receives a number of points corresponding to the number of candidates ranked lower. Once all votes have been counted, the option or candidate with the most points is the winner. a Range b Condorcet c Borda count d ApprovalConsider 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: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.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 isMr. 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?
- The proportion of commuters on PSU – Berks campus is purported to be 65%. A professor believes this to be inaccurate. He randomly selects 300 students on campus and determines 200 of them to be commuters. Can the professor reject the campus claim of 65%?Use the Borda count method to determine the winner of the election? Four students are running for president of the school: • Ariana (A), Brett (B), • Carlos (C), and • DeeDee (D). The 5 clubs and their members were asked to rank all candidates. Clubs 1 3 4 Number of Votes 19 15 11 7 2 First A B Second В A Third A C A Fourth D C В A В a A В d O O O OA Senior High School class held an election for class president. Instead of just voting for one candidate, the students needed to rank all the candidates according to preference. The table presents the results. RANKINGS Anton 2 3 1 3 4 2 Maria 4 1 3 4 1 3 Shelly 1 2 2 2 3 4 Troy 3 4 4 1 2 1 Number of Votes 36 53 41 27 31 45 1. Who is the winner by plurality? 2. What is the majority number of votes?
