PS 3 Midterm #1 Review WorksheetInduction vs. Deduction Compare and contrast these two approaches to the (social) scientific method. How do the steps to a good research design differ across these two approaches?Condorcet Tournament Imagine a congress of 430 members tasked with bestowing an honor on a previous head of state: Nikita, Leonid, Yuri, or Konstantin. The rules committee decides to vo
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PS 3 Midterm #1 Review Worksheet
Induction vs. Deduction
Compare and contrast these two approaches to the (social) scientific method. How do the steps
to a good research design differ across these two approaches?
Condorcet Tournament
Imagine a congress of 430 members tasked with bestowing an honor on a previous head of
state: Nikita, Leonid, Yuri, or Konstantin. The rules committee decides to vote using Condorcet’s
method to democratically select who should receive this supreme honor.
(a) How many possible preference orderings exist over these candidates? How many are
missing from the expressed preferences of the voters in the congress above?
(b) Determine the Condorcet winner, or explain why there is no Condorcet winner.
(c) How might the congress feel after the vote? Can you come up with a political take-away?
Historical bonus question: what legislative body might have been tasked with the vote?
Median Voter Theorem
Suppose we have customers with single-peaked preferences located on a one-dimensional line
that shows customer preference levels to a certain phone company. Suppose that customers
choose the telephone company located closest to them in distance and that they flip a fair coin if
two candidates are equally distant (so that we can count one-half vote for each candidate from
that voter). Further suppose that the seven customers are located as follows:
(a) Where should the two phone companies locate if they can locate anywhere they want to,
they know this distribution of voters, and they only care about maximizing profits?
(b) Two AT&T executives have different ideas for new promotions for their existing customers. If
they both offer their plans to customers with the goal of getting the most, at what preference
point(s) should they locate?
(c) If Verizon executives do the same thing, where should they locate to get the most
customers?
(d) If each company uses the winning promotion at the winning preference location, how many
customers will each company have?
Game Theory
Problem 1:
A firm (player 1) is considering entering an established industry with one incumbent firm
(player 2). Player 1 must choose whether or not to enter the industry. If player 1 enters the
industry then player 2 can either accommodate the entry or fight the entry by waging a price
war. Player 1’s most-preferred outcome is entering with player 2 not fighting, and its least
preferred outcome is entering with player 2 fighting. Player 2’s most-preferred outcome is
player 1 not entering, and its least-preferred outcome is player 1 entering with player 2
fighting.
Draw the game tree and find the equilibrium.
Problem 2:
In an authoritarian regime, there are two groups of citizens, the working class and the elite.
Each group has two strategies: revolt or stay home. Revolts weaken the ruling dispensation.
If both groups revolt, the dictator has to step down and democracy is introduced. If one
group revolts, the regime survives but becomes slightly weaker. Revolting alone is costly for
each group as the dictator remains in power and may end up punishing them.
(a). Suppose the players move simultaneously. Write out the normal form version of
the game. Show any Nash Equilibrium.
(c). Now suppose the players move sequentially. The elite moves first and the working class
decides whether to join the revolt or stay out. Write out an extensive form version of the
game. Solve by backward induction.
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