Directions: Based on the data provided below, answer completely the following questions. You must show ALL work in order to receive full credit. Your submission can be a handwritten write-up that is scanned and submitted as a PDF or JPG file or a typed write-up submitted as a DOC file. It must be submitted through the original case study link. The case study is worth 60 points.
Fifteen years ago, five friends opened The Cattle Crossing, a Texas ranch style restaurant. When making decisions, each owner has control over a different amount of votes based on how much money they originally invested in the restaurant. Chris controls 8 votes, Kara controls 6 votes, Bob controls 4 votes, Marie controls 3 votes, and Sam controls 2 votes. There needs to be 18 votes minimum in order to pass a decision.
- Show how the weighted voting system is denoted mathematically. (7 points)
- In the weighted voting system, determine which players, if any, are dictators, have veto power, or are dummies. (Appropriate work to show would be the 4 steps for checking these players like we did in our class notes.) (11 points)
- Use the Banzhaf power distribution to find the percentage of power each player holds. (18 points)
Kara has decided to retire and move to Florida. Since she is moving, she does not want any responsibilities at the restaurant anymore. Chris offered to buy her shares in the restaurant, and she agreed to this.
- Show the new weighted voting system with the four remaining players.
- Use the Shapley-Shubik power distribution to find the percentage of power each player holds for the revised weighted voting system in question 4.
Sample Solution