Question: Activity: 3. Thirteen students decide to vote on whether to play basketball B, soccer S, or volleyball V after school. Their preferences are given below:

Activity:

3. Thirteen students decide to vote on whether to play basketball B, soccer S, or volleyball V after school. Their preferences are given below: 5 4 2 2 1st choice B V S V 2nd choice S B V S 3" choice V S B B Find the winners using the different methods below (ties may occur): a. Plurality b. Borda method c. Pairwise comparison d. Plurality with elimination 4. For the weighted voting system [12: 8,6,5,3]: a. List all coalitions; identify which are winning coalitions. b. Determine the critical players in each winning coalition. c. Determine the Banzhaf power distribution for the system

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