The weighted voting system [8 : 6, 4, 2, 1] represents a partnership among four
ID: 3144202 • Letter: T
Question
The weighted voting system [8 : 6, 4, 2, 1] represents a partnership among four partners (P1, P2, P3, and P4). Partner 4 is the partner with just one vote, and in this situation, has no power. Not wanting to remain that way, Partner 4 offers to buy one vote. Each of the other partners is willing to sell P4 one of their votes and they are all asking the same price. From which partner should P4 buy in order to gain as much power as possible? Use the Banzhaf power index for your calculations. Explain your answer. Please help! The weighted voting system [8 : 6, 4, 2, 1] represents a partnership among four partners (P1, P2, P3, and P4). Partner 4 is the partner with just one vote, and in this situation, has no power. Not wanting to remain that way, Partner 4 offers to buy one vote. Each of the other partners is willing to sell P4 one of their votes and they are all asking the same price. From which partner should P4 buy in order to gain as much power as possible? Use the Banzhaf power index for your calculations. Explain your answer. Please help!Explanation / Answer
Hi, given vote shares are
[8; 6 4 2 1]
First we have to find the winning combinations from the above data.
A winning combination is the one where sum of votes is >=8
So, they are
AB,AC,ABC,ABD,ACD,ABCD
Now, we have to find the critical players from each of the above combinations, a critical player is the one on whose absense, the winning combination doesn't hold.
AB- both
AC- both
ABC- only a and b
ABD-only a and b
ACD- only a and c
ABCD- only a,
Total number of times of critical players=2+2+2+2+2+1=11
Now, check how many times each player is critical,
A- 6
B- 4
C- 1
Now,
BPI is,
For A 6/11
For B 4/11
For C 1/11
For D 0
Therefore since A has highest vote, it's best to take a vote from him.
Thumbs up if this was helpful, otherwise let me know in comments
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