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PP 202: Problem Set
• You should submit your problem set as a PDF on BruinLearn.
• You can work in small groups, but you should write every line of text or code that you submit.
1 Political games
A city council has 3 people on it. For a bill to pass, at least 2 must vote yes.
Suppose a bill comes up for a vote. All three council members would like the bill to pass. But the bill is unpopular
with many voters, so they would ideally like it to pass without having to personally vote yes.
In particular, each council member’s ranking of outcomes is this:
• Best outcome (i.e., highest payoff): Vote no but have the bill pass.
• 2nd best outcome: Vote yes and have the bill pass.
• 3rd best outcome: Vote no and have the bill fail.
• Worst outcome (i.e., lowest payoff): Vote yes and have the bill fail.
Abstentions are not allowed, each council member must either vote yes or no. Voting occurs simultaneously.
1. How many voting outcomes (i.e., strategy profiles) are there in this scenario?
2. Suppose Member 1 thinks both other members will vote Yes. What is Member 1’s best response?
3. Suppose Member 1 thinks one other council member will vote Yes and one will vote No. What is Member
1’s best response?
4. Is it a Nash Equilibrium for Members 1 and 2 to vote Yes and Member 3 to vote No?
5. Is it a Nash Equilibrium for Member 1 to vote No and Members 2 and 3 to vote Yes?
6. Is it a Nash Equilibrium for all three council members to vote Yes?
7. Is it a Nash Equilibrium for all three council members to vote No?
8. Imagine you are advising Member 1. What would you advise Member 1 to do in the run up to the vote?
(Write a short paragraph.)
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2 Election post-mortem
The Republican National Committee (RNC) has hired three consultants and asked them to determine the cause
of their loss in the 2020 presidential election.
• Consultant 1: “Republicans did not do enough TV advertising.”
• Consultant 2: “Republicans should not have criticized mail-in voting, which depressed turnout.”
• Consultant 3: “President Trump should have done a better job containing COVID-19.”
The RNC is confused by these conflicting claims about the cause of their 2020 loss. They hire you to adjudicate
between these three possibilities and tell them which is the true cause. What would you tell them? How would
you suggest they proceed?
Your answer should be 1-2 paragraphs (max: 400 words).
3 Selection bias in the wild
Find an example of a journalist or policymaker who you believe has wrongly interpreted a correlation as evidence
of a causal relationship. First, describe the comparison that the journalist or policymaker relies on and, second,
explain why you think this correlation is not persuasive evidence of a causal relationship. If you think the rela-
tionship is confounded, be specific about potential sources of confounding. If you think reverse causality may
be at play, explain how that would work.
Your answer should be 1-2 short paragraphs (max: 400 words). Include a link to the source you are critiquing.