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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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.
Transcribed Image Text: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.
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