ECOS3020/ECON6101: Political Economy
Anastasia Burkovskaya and Ashani Amarasinghe
Homework I
1. Finish the proof of May’s theorem from lecture 1, i.e., show that when n+(α1, . . . , αN ) <
n?(α1, . . . , αN), then F (α1, . . . , αN) = ?1.
2. Which of the May’s axioms is broken in each of the following cases?
(a) a guilty verdict in a criminal case requires unanimity of the jury;
(b) IMF voting is weighted according to member contributions.
3. Show that instant-runoff voting and round-robin tournament do not satisfy the IIA and MIIA
axioms.
4. Suppose local councils spend money only on roads and clean water. The share of the expen-
ditures for clean water is α ∈ [0, 1]. Voter preferences are Ui = ?|α? pi|, where pi is the bliss
point of voter i. Suppose for men pi ～ U [0; 0.75] (uniform distribution), whereas for women
pi ～ U [0.25; 1]. There are equal shares of men and women in the population.
(a) Are these preferences single-peaked?
(b) What is the policy outcome if only men can vote?
(c) What is the policy outcome if everyone can vote?
(d) Which outcome does better represent what women want?
5. Consider Meltzer and Richards (1981) model with only two types of income: yp (poor) and yr
(rich). Normalize population to 1 with the share of rich being δ < 0.5. Average income is yˉ.
To focus on inequality and distributional conflict, we add inequality into the model directly:
Denote by θ the share of the total income directed onto the rich, i.e., yr = θyˉ
δ
(income per rich
person) and yp = (1?θ)yˉ
1?δ (income per poor person). So an increase in θ represents an increase
in inequality. Also we must have θ > δ (so yp < yˉ < yr). The government is going to use
income tax rate τ and taxation is costly as before with DWL 0.5τ 2 per person.
(a) Suppose the tax collected from the population is distributed as a lump-sum subsidy to
everyone. What is the bliss point for the rich? for the poor?
(b) Who represents the median voter in this model? What will be the tax? How does it
depend on θ?
(c) Define the burden of taxation as the net redistribution away from the rich. How does it
depend on θ?
(d) Now suppose the collected revenue is distributed as lump-sum only to the poor. What
will be the tax? Compare it with the previous case without targeted transfers. How does
the tax depend on θ?
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(e) Find the burden with the targeted transfer. How does it compare with the case without
the targeted transfer? Which of the situations has greater degree of conflict in the
society?
6. Consider the ethical-voter model, but suppose that the density of μ is f(μ) = 2μ on [0, 1].
Derive the equilibrium cut-off levels for both groups. (You can check the answer in the lecture
slides.)
7. Give an example of manipulability of the Borda count and Coombs system.
8. Consider the key seat of Macnamara in 2022 Federal elections:
Come up with an example of different preferences and strategic voting if the first preferences
have this distribution.
9. Prove the Theorem from Degan (2007) discussed in the lecture that defines the voting strategy
of a voter who cares about candidate’s valence and might be informed or uninformed.
10. Consider the empirical exercise in von Hohenberg & Hager (2022).
(a) Explain in layman’s terms the research question examined in this paper. Use no more
than 3 sentences.
(b) Discuss the intuition underlying the identification strategy used to answer this research
question.
(c) To what extent can these estimates be interpreted causally? Give reasons for your answer.
(d) If you were to design an empirical strategy to examine this research question to derive
causal estimates, what would you do differently?
(e) What do the authors propose as the mechanism underlying the baseline effect? Can you
think of any other potential mechanisms that can be relevant in this context?