POL 407 Midterm Exam FALL 2004
Name: ______
1. Imagine the following scenario (assume single-peaked utility functions):
M φ
______
| | | |
D L C R
Here, D is the Democratic leadership’s position; L is the ideal point for some Democratic legislator; C is the ideal point for legislator L’s constituency (i.e. the ideal point for the constituency’s median voter), and R is the Republican leadership’s position. Suppose that the status quo position is at φ and the Democratic leadership proposes alternative M. Assume that L is equidistant from D and R.
Suppose that the Democratic leadership wants M passed (i.e., this is a very, very important vote for the Democrats) and that they need L’s vote to win. Explain the problem this scenario poses for the Democratic leaders, at least with respect to L. If the Democratic leadership did nothing, which position would L support and why would L take this position? What are the political problems facing L when it comes to deciding how to vote? (10 points)
2. Suppose that there are three students who are trying to choose where to go for Spring Break. The students, A,B, and C, have the following preference orderings over destinations (the destinations are: Rocky Point [RP]; Daytona Beach [DB]; Las Vegas [LV]):
A: RP>DB>LV
B: DB>LV>RP
C: LV>RP>DB
Given this scenario and assuming round-robin voting, please answer the following questions.
a. What is the group’s preference ordering? (4 points)
b. Is this ordering a Condorcet winner (why or why not)? (4 points)
c. Suppose that instead of Spring Break destinations, the alternatives were: Leftist Candidate, Centrist Candidate, Rightist Candidate in a three-party election. Assuming sincere preferences and non-strategic voting, would the assumption of universal admissibility be a reasonable assumption to make for these alternatives? Why or why not? (4 points)
3. The “rationality assumption” we have adopted states the following:
_____ A. Preferences are complete and transitive.
_____ B. Preferences are incomplete and intransitive.
_____ C. Preferences reflect societal values.
_____ D. Preferences are at the median.
4. The condition of “universal admissibility” says that:
_____ A. Some preference orderings are not allowed.
_____ B. Any intransitive preference ordering is allowed.
_____ C. Any transitive preference ordering is allowed.
_____ D. There exists no dictator.
5. The condition of “Pareto Optimality” says that:
_____ A. Any transitive preference ordering is sufficient to produce an optimal outcome.
_____ B. If jk for each individual in a group, then the group must prefer jk..
_____ C. If j>k for each individual in a group, then the group will cycle to k>j.
_____ D. There exists no mechanism to jointly improve each individual’s utility.
6. The condition of “independence from irrelevant alternatives” says that
_____ A. The relationship between two alternatives, j and k is unaffected by a third alternative, l.
_____ B. The relationship between two alternatives, j and k is altered by a third alternative, l.
_____ C. If j>k for each individual in a group, then the group will cycle to k>j.
_____ D. Any added alternatives have no impact on group choice.
7. The condition of “nondicatorship” says that:
_____ A. Dictators are non-democratic.
_____ B. Dictators are necessary to stop cycling preferences.
_____ C. There exists no individual whose own preference determines the group’s preference.
_____ D. None of the Above
8. Imagine the following scenario:
______
0 100 200 300 400
SQ
ASUA BofR Likins Jones Fac. Sen.
Suppose there are 5 voters, an ASUA representative, a Board of Regents Representative, UA President “Likins”, some professor named Jones, and representative from the Faculty Senate. They are voting on a tuition increase. The status quo (“SQ”) is a $0 increase. The ideal points for the other voters are above. Assume they are evenly spaced on the line and have symmetrical utility functions. Assume also that majority voting holds and that each voter can propose an alternative. Answer the following questions (a—d: 4 points each; e: 10 points)
a. Round 1: The Board of Regents representative proposes his ideal point. What would the outcome be (who would support his position and who would support the status quo? Is there a new status quo position after round 1?)
b. Round 2: Now suppose that the Faculty Senate rep. proposes her ideal point ($400). In a pairwise vote of this alternative versus the status quo from Round 1, what would the outcome be (who would support her position and who would support the status quo? Is there a new status quo position after round 2?)
c. Round 3: Now suppose Likens proposes his ideal point ($200). In a pairwise vote of this alternative versus the status quo from Round 2, what would the outcome be (who would support his position and who would support the status quo? Is there a new status quo position after round 3?)
d. Round 4: Suppose Professor Jones proposes his ideal point ($300). ). In a pairwise vote of this alternative versus the status quo from Round 3, what would the outcome be (who would support his position and who would support the status quo? Is there a new status quo position after round 4?)
e. What does this game illustrate? That is, what is the most important lesson learned from this game and why?
9. What is the relationship between Condorcet’s Paradox and Arrow’s Theorem? (8 points)
10. What is the relationship between Down’s spatial model of elections and Black’s median voter theorem? (8 points)
11. Assume there are 5 possible grades a student can earn: A,B,C,D,E, where “E” denotes a failing grade.
a. Draw a picture of a utility function for student grades. (3 points)
b. Why is the utility function single-peaked? (3 points)
12. Consider the following unidimensional spatial model:
| | |
C φ,R M
In this model, “C” denotes the median ideal point for a legislative committee; φ denotes the status quo policy, R denotes the ideal position of the “Rules” Committee, and M denotes the chamber median (i.e. the median ideal point for all of the legislators in the chamber). Assume that the Rules Committee’s ideal point= φ. Suppose that in this institution, the Rules Committee can do one of three things: 1: issue “open” rules where the committee’s proposal “C” can be amended in any way; 2. issue “closed” rules where the committee’s proposal “C” cannot be amended at all; 3. refuse to issue a rule which means that the committee’s proposal “C” cannot be heard on the floor of the legislature. .
a. Where would policy end up being located if an open rule were adopted? (3 points)
b. Where would policy end up being located if a closed rule were adopted? (3 points)
c. Where would policy end up being located if no rule were adopted (i.e. the Rules committee refuses to issue a rule)? (3 points)
d. Given the legislative committee’s preference for C, which action from the Rules Committee would most benefit the legislative committee (i.e. “open,” “closed,” or “refuse to issue a rule”) and why? (4 points)
e. Given the Rules Committee’s preference for φ and the legislative committee’s preference for C, what kind of action would most benefit the Rules committee (i.e. “open,” “closed,” or “refuse to issue a rule”) and why? (4 points)