Question

Problem 5 Consider a community of 11 individuals that has to decide the size G of a public project. Among the 11 people, 4 people (type 1) have a marginal benefit (net of cost, i.e., you can think that costs are zero) for the public project MB1(G) = 2 – 2G 2 people (type 2) have a marginal benefit MB2 (G) = 12 – 6G, and 5 people (type 3) have a marginal benefit MB3 (G) = 4 – G. Assume that for some technical reason, there are only three alternatives for G:Gs = 0.8, GM = 2.1, and GL = 4.3. Assume that people vote sincerely (i.e., naively). i) Find the favorite option for types 1, 2, and 3 respectively. (Hint: The answer is not very difficult as long as you avoid trying to fit it to some easy recipes. It may help to draw a graph with marginal benefit functions for these options.) ii) Which of the three alternatives will be chosen under sequential ma- jority voting? Does the outcome depend on the order in which the votes are taken? iii) Now suppose the three alternatives are voted on at the same time and the one that gets the most votes will be chosen. What is the outcome? (Assume naive voting for this question). iv) Now suppose the decision is made in two rounds as follows. In the first round, the three alternatives are voted on as in b). Then, the one that obtained the least votes is eliminated. In the second round, people vote on the remaining two alternatives. What is the outcome? (Assume naive voting)

Answer 1

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