ECON3106 Politics and Economics
ECON3106 Politics and Economics
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ECON3106 Politics and Economics
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
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.,∑
i∈{1,50,100}
ui (A)?
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?