Problem
You may apply the following three Theorems in Simple majority voting in solving the problems:
median voter theorem
cyclical majority - Condorcet paradox
fiscal commons
Part A.. Consider a community of three persons, I, II, and III. They consider collective decision on public education. A majority of the members must approve all decisions. (in this case two out of three persons must agree.) The three alternatives are H, M, and L, where H is large amount, M is middle amount and L is low amount of spending in education.
Suppose each individual ranks for the three alternatives in the following way:
I: H > M > L (I.e., person I prefers H, high amount in education, most, then, middle, then low amount)
II: M > L > H
III: L > M > H
Q1. Can you apply the Median Voter Theorem to this problem? To justify your answer, state the conditions under which the MVT holds and show whether the conditions are met.
Q2. Suppose person - I is a high income person who may consider an alternative for children's education. That is, if the voting result is M or L, he wants to send his children to a private school. Even if he does not get benefit from public education, he still has to pay tax for public education. He would prefer to pay less tax. Thus, his preference ordering now becomes,
I: H > L > M.
What is the result of the simple majority rule by pairwise comparison?
Part B. We want to understand the effect of majority rule on budget size. Three politicians 1, 2, and 3 represent different regions. They will finance public goods by imposing a general tax equally on all residents in different regions. Assume that regions are of equal size. Three spending projects are A: bridge in region 1; B: bridge in region2; C: bridge in region 3. Each project costs $300 million. For each project, the tax bill per region will be $100 million. The benefits of projects A, B, C are as follows.
A B C
Benefits to 1 120 80 0
Benefits to 2 120 0 150
Benefits to 3 0 250 150
Q1. Suppose the decision is made by a simple majority vote on an item-by-item basis. Which project will pass? What is the total budget size? Is if efficient?
Q2. Now treat all three projects simultaneously as a combined budgetary package. What would be the voting result?
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.