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:
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- 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 (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[32: 10,6,6,5,4,4,3,2,1]Find:The total number of players: The total number of votes: The quota: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: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?
- 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?A group of military officers is composed of 6 Army Officers, 7 Navy Officers, and 8 Air Force Officers. An eight officer committee is to be randomly selected. Find P(2 Army Officers, 2 Navy Officers, 4 Air Force Officers).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
- Last year at a certain high school, 11 students sought the nomination for president of the student body. In how many ways could the voters (student body) rank their first 4 choices?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 OUse the Condorcet 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. Number of Voters Preference Order 1st to last 19 A C D 15 В D A C 11 D A C В 7 D В A D A В a A b В C d No Condorcet winner O O O O