The Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2.
What is the distribution?
The mathematical expression known as a distribution function expresses the likelihood that a system would adopt a certain value or range of values. The traditional examples include games of chance.
List of winning coalitions:
1. P1, P2, P3
2. P1, P2
3. P1, P3
No. of times P1 is critical = 3 (P1 is critical all 3 times as it has veto power)
No. of times P2 is critical = 1 (in the second coalition)
No. of times P3 is critical = 1 (in the third coalition)
Total no. of critical times = 3 + 1 + 1 = 5
Banzhof Power Distribution:
Player 1: No. of times P1 is critical/Total no. of critical times
= 3/5 = 0.6
Player 2: No. of times P2 is critical/Total no. of critical times
= 1/5 = 0.2
Player 3: No. of times P3 is critical/Total no. of critical times
= 1/5 = 0.2
Hence, the Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2
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