Sample+Quiz_2

# Sample+Quiz_2 - yes or no Critical players{P1,P2 7 5=12 Yes...

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Dear Students, You will have a quiz on Friday, February 11. One of the problems on the quiz will be like the problem that we did in class, but with different numbers. I will give you 2 empty tables to fill in. Please see file called Sample Quiz #2 which has the problem we did in class and the solution. In this file you will also see how the problem will be presented on the quiz. Sample Problem #1 for Quiz #2. Find the Banzhaf power distribution in the weighted voting system [12: 7, 5, 3, 2] Coalition Weight Winning yes or no Critical players Banzhaf power index P 1 P 2 P 3 P 4 Answers on next page:

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Answers. You will fill in the table. Coalition Weight Winning
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Unformatted text preview: yes or no Critical players {P1,P2} 7+5=12 Yes P1 and P2 {P1,P3} 7+3=10 No {P1,P4} 7+2=9 No {P2,P3} 5+3=8 No {P2,P4} 5+2=7 No {P3,P4} 3+2=5 No {P1,P2,P3} 7+5+3=15 Yes P1 and P2 {P1,P2,P4} 7+5+2=14 Yes P1 and P2 {P1,P3,P4} 7+3+2=12 Yes P1, P3,and P4 {P2,P3,P4} 5+3+2=10 No {P1,P2,P3,P4} 7+5+3+2=17 Yes P1 There are 10 instances of some player being critical. In 5 of those instances, P 1 is critical, in 3 instances P 2 is critical, once P 3 is critical, and once P 4 is critical. Thus the Banzhaf power distribution is as follows: Banzhaf power index P 1 5/10 = 50% P 2 3/10 = 30% P 3 1/10 = 10% P 4 1/10 = 10%...
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## This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

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Sample+Quiz_2 - yes or no Critical players{P1,P2 7 5=12 Yes...

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