6. 0/6 points | Previous Answers My Notes Ask Your Teacher A father and his thre

Question

6. 0/6 points | Previous Answers My Notes Ask Your Teacher A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index

Explanation / Answer

(a) There are two situation to chosse a activity from aplay or a movie.

If out of four, three is agree for a particular activity, then they do it.

The winning coalitions are there when majority of a particular game is more.

i. 3 children ii. two children + one Father, it is three times, iii. one children, one father , it is also three times

TOtal winning coaltions is 1+3+3 =7

(b)

the children's Banzhaf power index is 7/16

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