1. If Candidates , , and receive 55, 47, and 10 votes, respectively, what percentage of the votes does each candidate receive? If the Democratic Delegate Selection Rules are used to award delegates, will one of the candidates lose his or her support? Which one and why?

2. In Skills Check 1, Candidate is dropped from the election. Calculate the adjusted percentages of the popular vote for Candidates and .

3. If Candidate receives 14,056 of the 23,903 votes and the district has 12 delegates to award, then what is Candidate ’s quota?

4. Candidates , , , and have quotas of 5.32, 3.92, 3.36, and 1.4, respectively. Use Hamilton’s method to award the 14 delegates.

5. If the number of delegates to be awarded for the election in Skills Check 1 is 20, then how many delegates will each candidate receive? (Use Hamilton’s method, but do not use the Democratic Delegate Selection Rules.)

6. If the number of delegates to be awarded for the election in Skills Check 1 is 20, then how many delegates will each candidate receive? (Use the Democratic Delegate Selection Rules.)

7. If five voters have ideal points 4, 5, 5, 6, and 9, then what is the median of the distribution of their ideal points?

8. If six voters have ideal points 4, 5, 5, 6, 9, and 10, then what is the extended median of the distribution of their ideal points?

9. Give an example of an even number of ideal points where the extended median is a single value, as opposed to an interval.

10. For a discrete distribution of voters’ ideal points and an odd number of voters, can there be more than one equilibrium position? Explain.

11. Explain why, for a discrete distribution of voters’ ideal points and an even number of voters, there can be more than one equilibrium. Must there be more than one equilibrium? Explain.

12. In a two-candidate election, suppose the attitudes of the voters are distributed symmetrically around the median . Of the two candidates, and , is positioned far to the left of , and is positioned just to the right of . Which, if either, candidate will receive more votes?

13. In a two-candidate election, suppose that the attitudes of the voters are skewed to the left of the median , so they are more spread out to the left than to the right. Assume that Candidates and take positions to the left and right of , respectively, so that there are the same numbers of voters between their positions and . Candidate __________ will receive a majority.

14. In a two-candidate election, which of the following positions is an equilibrium position for both Candidates and ?

15. Assume that and take distinct equidistant positions from the median of a symmetric distribution (not necessarily unimodal), with half the voters between the announced policy positions of and . Which of the following statements is true?

16. In a three-candidate election, suppose the attitudes of the voters are distributed symmetrically around the median . Of the three candidates, , , and , is positioned far to the left of , is positioned just to the right of , and is positioned at . Candidate ____________ will receive the most votes.

17. Suppose that Candidate is situated so that exactly 1/3 of the voters lie to his left. In a two-candidate race, if Candidate must remain fixed, Candidate —to maximize her vote total—should situate herself

18. In a three-candidate election, if Candidates and are positioned at , the election-winning position of Candidate is ________________.

19. In a three-candidate election, if Candidates and are positioned just to the left and just to the right of , are there election-winning positions for Candidate ? What are they?

20. In a four-candidate election, if candidates are aligned in order , Candidate __________ benefits if drops out of the race.

21. In a five-candidate election, if candidates are aligned in order and each receives about 20% of the vote, Candidate ________ benefits most if Candidates , , and drop out.

22. Suppose that the distribution of voters’ ideal points is symmetric and that two candidates have announced positions on opposite sides of and equidistant to the median such that there is no 2/3-separation opportunity. Would a third candidate that enters with a policy position farther from the median be a spoiler?

23. What is the median of 3, 3, 4, 4, 4, 5, 6, 6, 6, 6, 6? How does this compare with the weighted median of 3, 4, 5, and 6 with associated weights of 2, 3, 1, and 5?

24. True or False: The median-voter theorem is the special case of the weighted median-voter theorem in which all weights are 1.

25. If states , , and have median positions on a left-right spectrum of 25, 32, and 28, respectively, and the states have 3, 5, and 3 electoral votes, respectively, then what is the weighted median?

26. How does the proposed use of awarding electoral votes based on votes in electoral districts compare with how delegates are awarded in primaries?

27. The National Popular Vote law is a

28. If states with a majority of electoral votes passed the National Popular Vote law, it would be impossible for a candidate for president to win the popular vote and yet lose the Electoral College because ___________.