217k views
0 votes
Consider the voting scheme [6:4,2,2,1] select the correct Banzhaf power distribution 7 winning coalitions.

a) [0.5, 0.5, 0, 0]
b) [0.25, 0.25, 0.25, 0.25]
c) [0.6, 0.2, 0.2, 0]
d) [0.4, 0.3, 0.2, 0.1]

1 Answer

3 votes

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.

User Michael Burdinov
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories