ECON3106 Politics and Economics Problem Set 1
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ECON3106 Politics and Economics
Problem Set 1
1 .
A society is composed of 3 individuals: i, j, k . There exists 4 alternatives: A, B, C, D . Individual preferences are given by
A >i B >i C >i D
B >j D >j C >j A
A >k B >k C >k D .
For each of the methods below, find the resulting social ranking.
1.1 Start with the entire set of alternatives and count how many voters prefer each alternative the most. If one alternative is preferred the most by more individuals than any other alternative, then place this alternative at the top of the social ranking. Now consider only the set of remaining alternatives and repeat the process to find the second best alternative in the social ranking. Continue until all alternatives are ranked.
1.2 First, each individual eliminates the alternative he or she prefers the least. If more than one alternative is eliminated, place last the one eliminated by more individuals. Repeat until you have ranked all alterna- tives.
You might have noticed that both systems violate Universal Domain.
1.3 With an example with three individuals, i, j, k, and three alternatives, A, B, C, show that the system in
1.2 violates Universal Domain.
2 .
A society is composed of 3 individuals named 1, 50, and 100. There are three alternatives: 2, 60, and 90. For each individual i ∈ {1, 50, 100}, her utility from alternative A ∈ {2, 60, 90} is given by
ui (A) = − |i − A|
where |x| is the absolute value of x.
2.1 How does each individual rank the three alternatives?
2.2 Which alternatives are Pareto efficient?
2.3 Which alternatives maximize social surplus, i.e.,
ui (A之,
i∈{1_50_100}
Assume that voters vote sincerely.
2.4 Consider a majority vote between alternatives 2 and
60. Which alternative would win?
2.5 Consider a majority vote between alternatives 60 and
90. Which alternative would win?
2.6 Consider a majority vote between alternatives 2 and
90. Which alternative would win?
2.7 Suppose we used the Open Agenda Method. Which alternative would be chosen?
2023-06-28