A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What is the minimum number of votes required to pass a bill?
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A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What is the minimum number of votes required to pass a bill?
ANSWER: 6
Given the scenario previously mentioned, how many coalitions are possible?
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Given the scenario previously mentioned, how many coalitions are possible?
Given the same scenario, list all possible coalitions with voting bodies A, B, C and D. Be sure to include their point totals! Try and do this in an orderly fashion!
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Given the same scenario, list all possible coalitions with voting bodies A, B, C and D. Be sure to include their point totals! Try and do this in an orderly fashion!
{ }AB;5ABC;6ABCD;10 A;3AC;4ABD;9 B;2AD;7ACD;8 C;1BC;3BCD;7 D;4BD;6 CD;5
A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What are the winning coalitions? Write you answers like { A,B,D;10}
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A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: What are the winning coalitions? Write you answers like { A,B,D;10}
ANSWER: { A,B,C;6} {A,B,C,D;10} {B,C,D;7} {A,C,D;8} {A,B,D;9} {B,D;6} {A,D;7}
A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Find the power index for each province.
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A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Find the power index for each province.
ANSWER: A = 3 B = 3 C = 1 D = 5
What % of the vote does D have? What % of the power does D have?
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What % of the vote does D have? What % of the power does D have?
A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Name the dummies and/or dictators.
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A small country has 4 provinces – A, B, C and D. Each province contains 30%, 20%, 10% and 40% of the population in the country, respectively. The number of votes assigned to each province is: A – 3 B – 2 C – 1 D – 4 Under the current legislative process, a bill can pass by a simple majority vote. Q: Name the dummies and/or dictators.
ANSWER: There are no dummies or dictators
Determine whether any voter is a dictator and whether any is a dummy. A – 10 votes B – 8 votes C – 6 votes D – 3 votes 20 votes are needed to pass an issue
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Determine whether any voter is a dictator and whether any is a dummy. A – 10 votes B – 8 votes C – 6 votes D – 3 votes 20 votes are needed to pass an issue
No one is a dictator because no one has 20 or more votes AND No dummies because each voter is essential in at least one winning coalition
Determine whether any voter is a dictator and whether any is a dummy. A – 20 votes B – 10 votes C – 8 votes D – 1 votes 20 votes are needed to pass an issue
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Determine whether any voter is a dictator and whether any is a dummy. A – 20 votes B – 10 votes C – 8 votes D – 1 votes 20 votes are needed to pass an issue
A is a dictator because it has 20 votes and 20 votes are needed to pass the issue AND B, C and D dummies because they don’t have enough points to pass and issue
A corporation has 4 shareholders and a total of 60 shares. Each share is worth one vote. The # of votes needed to pass an issue is a simple majority. The # of shares are as follows: A – 27 B - 15 C - 12 and D - 6 The winning coalitions are [A,B; 42] [A,B,C; 54] [A,B,C,D; 60] [A,C; 39] [A,B,D; 48] [A,D; 33] [A,C,D; 45] [B,C,D; 33] The power indexes are as follows: A = 6 B = 2 C = 2 D = 2 B owns 25% of the shares. What fraction of the power does B have?
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A corporation has 4 shareholders and a total of 60 shares. Each share is worth one vote. The # of votes needed to pass an issue is a simple majority. The # of shares are as follows: A – 27 B - 15 C - 12 and D - 6 The winning coalitions are [A,B; 42] [A,B,C; 54] [A,B,C,D; 60] [A,C; 39] [A,B,D; 48] [A,D; 33] [A,C,D; 45] [B,C,D; 33] The power indexes are as follows: A = 6 B = 2 C = 2 D = 2 B owns 25% of the shares. What fraction of the power does B have?
2/12 = 1/6
Question #:
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If each person approves of their first 3 choices, who is the winner using the approval method?