Overview
Try to apply these if you can
- Condorcet’s Paradox
- Condorcet cycle (cyclical or cycling majorities)
- Condorcet winner
- Strong preference orderings
- Distributional politics (“divide the dollars”)
- Arrow’s (Impossibility) Theorem and its conditions
- May’s Theorem and its conditions
- Black’s Single-Peakedness Theorem
- Sen’s Value-Restriction Theorem
1) Your university department needs to make a decision about hiring a new faculty member. These decisions have been notoriously difficult in the past, with the hiring committees unable to come to decisions. Every member of your department is strong-willed and independent; each of them sees the field and the department’s priorities differently from everyone else. The plan is for a four-person committee to choose among five candidates. Given your expertise with group choice, you have been asked to make one and only one change to this plan in order to make a hiring decision more likely. What change do you propose and why?
2) For each of the situations described here, identify which of the conditions of the Method of Majority Rule (here N, A, and M from Mays’ Theorem) is violated. You may find it useful to think about why these departures were seen as desirable, but this is not a required part of your answer.
- a) Conviction on impeachment requires two-thirds support in the United States Senate.
- b) The International Monetary Fund (IMF) uses a system of weighted voting where weights are determined by contributions to IMF operating funds. For example, the US has 17% of voting rights, while Germany has 5% and Saudi Arabia has 2%.
- c) The French president is elected under two-stage majority rule. In the first round all parties’ candidates compete against each other. If no candidate gets a majority in this round, the top two vote-getters compete against each other in a second round.
3) Below you see the preference orderings of two different societies. You can think of the societies as each consisting of only three members or you can think of each of the members of the society having one of the three listed preference orderings. This makes no difference. For each of the societies, state whether the preferences satisfy Sen’s value-restricted condition (for any three options, all voters have to agree that at least one is first or last or in the middle). If the society fails to satisfy this condition, identify the tuple or tuples that violates this condition.
Society 1:
yP1xP1zP1w
wP2yP2xP2z
zP3yP3wP3x
Society 2:
yP1wP1zP1x
wP2xP2yP2z
zP3wP3yP3x