ch16_solutions_solved edit

ch16_solutions_solved edit - Solutions to Chapter 16...

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Solutions to Chapter 16 Exercises SOLVED EXERCISES S1. Under truthful voting, A should match Geology and Sociology in the first vote, with the winner (Geology) to face Philosophy in the second round. Under strategic voting, A should match Philosophy and Sociology in the first round. In order to prevent a Geology outcome, B casts a strategic vote for Philosophy; Philosophy goes on to beat Geology. S2. Allocate points in the following way: 5 for a first-place vote, 2 for a second-place vote, and 1 for a third-place vote. A then receives 5 + 5 + 1 + 1 = 12 points, B gets 2 + 2 + 5 + 2 = 11, and C gets 1 + 1 + 2 + 5 = 9. S3. (a) Under a plurality voting system (with truthful voting), Proposal 1 gets 20 votes and Proposals 2 and 3 get 15 votes each. (b) Under a 3-2-1 Borda count with truthful voting, Proposal 1 gets 60 + 15 + 30 = 105 points, Proposal 2 gets 40 + 45 + 15 = 100 points, and Proposal 3 gets 20 + 30 + 45 = 95 points. (c) For both the second and third type of voter to gain, Proposal 3 must win rather than Proposal 1. This can be achieved if types 2 and/or 3 change their votes in such a way that Proposal 1 gets fewer points and/or Proposal 3 gets more. One example would be if types 2 and 3 vote as though their rankings were Proposal 3, Proposal 2, Proposal 1. With this voting pattern, Proposal 1 gets 60 + 15 + 15 = 90 points, Proposal 2 gets 40 + 30 + 30 = 100, and Proposal 3 gets 20 + 45 + 45 = 110. Note two things. First, other voting schemes will also result in Proposal 3’s winning. For example, if only the type 2s vote with a 3-2-1 ranking, Proposal 3 still wins. Second, a single member of types 2 or 3 can’t alter the outcome by changing only her vote; coordinated action is required. S4. (a) The preferences create a standard intransitive ordering, so none of the three alternatives would win a majority vote with truthful voting. (b) This example is virtually identical to the three councillors example in the text in Sections 2.A, 2.B, and 4.B. Let Soft here be equivalent to Generous (G) in the City Council example, let Medium Solutions to Chapter 16 Exercises 1 of 4
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= Average (A), and let Hard = Decreased (D). Then the civilian doves play the role of the left types on the
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ch16_solutions_solved edit - Solutions to Chapter 16...

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