Social Choice_Problem Set 8

Social Choice_Problem Set 8 - Social Choice Manipulation...

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Social Choice: Manipulation and Analysis (Econ 497/ Econ 597) Problem Set 8: Power in voting 1. Suppose there are 5 men and 7 women. (a) How many di/erent ways can we arrange these 12 people in a line? (b) How many di/erent committees of 4 people can be formed? (c) How many di/erent committees of 4 committees can be formed with exactly two men and two women? (d) How many di/erent committees of 6 committees can be formed with exactly 3 men and 3 women? 2. Suppose we have a weighted voting system with 5 voters °named A, B,
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Unformatted text preview: C, D, and E. The voters have the following number of votes: A 8 Votes B 6 Votes C 4 Votes D 2 Votes E 2 Votes Passage of a bill requires 18 votes. (a) Find all of the winning coalitions. (b) Calculate the Banzhaf Index of Power for each of the 5 voters. (c) (5 Points) Calculate the Shapley-Shubik Index of Power for voter C. Hint: 5!=120. ..Don±t try and do this the long way! 3. Explain why the ²Beautiful Chart Method³works in the computation of the Banzaf Index of Power. 1...
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  • Spring '12
  • Vanessen
  • English-language films, Voting system, Plurality voting system, votes, di¤erent committees

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