Final answer:
The correct Banzhaf power distribution for the voting scheme [6:4,2,2,1] among 7 winning coalitions is option (c) [0.6, 0.2, 0.2, 0]. This reflects the voting power of each voter based on their ability to change the outcome from a loss to a win.
Step-by-step explanation:
The question asks us to consider the voting scheme [6:4,2,2,1] and select the correct Banzhaf power distribution among 7 winning coalitions. The voting powers are distributed among four voters with voting weights of 6, 4, 2, and 1 respectively. The Banzhaf power index is a measure of the voting power of a voter in a decision-making body. It accounts for the number of times a voter can change an outcome from a loss to a win by joining a coalition. In this case, we need to calculate the power distribution by identifying the critical votes, which are votes where the voter is pivotal in achieving a winning coalition.
To find the correct distribution, we analyze each voter's ability to affect the outcome:
- Voter 1 (with 6 votes) can be pivotal in every possible winning coalition. They have total control.
- Voters 2, 3, and 4 (with 4, 2, and 1 vote respectively) can be pivotal, but less frequently than Voter 1.
Considering this, the correct Banzhaf power distribution that reflects the relative power of each voter is option (c) [0.6, 0.2, 0.2, 0]. It represents that Voter 1 (with 6 votes) has the most power, and Voter 4 (with 1 vote) has no power in changing the outcome.