Exam 12: Electing the President

Define an equilibrium position.

Use the following to answer the Questions A distribution of voters is uniform over [0, 1]. Candidates A and B have already entered the election and have chosen positions at 1/4 and 3/4, respectively. -If C enters at 1/3, what fraction of the vote does the winner receive?

Use the following information to answer the Questions Five board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 4), (5, 2), (6, 4), and (6, 2). Assume that A and B announce policy positions of (1, 2) and (5, 4), respectively. -What is the equation of the line passing through candidates' policy positions?

Describe the spoiler problem.

Use the following distribution of 33 voters at eight different positions over the interval [0, 1] to answer Questions Position 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Number of voters 1 4 6 6 6 2 5 3 -What is the equilibrium position in a two-candidate election?

The Electoral College is designed to enable the most popular candidate to win election.

Use the following information to answer the Questions Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 5), (3, 3), (5, 2), (6, 4), (6, 2), (4, 4), and (3, 2). Assume that A and B announce policy positions of (2, 2) and (5, 4), respectively. -Find the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A.

Use the following information to answer the Questions Consider the following distribution of 35 voters at eight different positions over the interval [0, 1]. Location 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Number of voters 4 7 4 2 3 7 4 4 -Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.7. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

Use the following information to answer the Questions Consider the following distribution of 34 voters at eight different positions over the interval [0, 1]. Location 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Number of voters 3 6 7 4 3 4 4 3 -Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.8. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?

Suppose 20 voters are distributed at different positions over the interval [0, 1], as shown below. Location 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Number of voters 2 0 4 5 4 1 0 0 0 What is the median position of the voters?

Use the following information to answer the Questions Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively. -What is the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A?

Use the following distribution of 31 voters at seven different positions over the interval [0, 1] to answer the Questions Position 0.1 0.2 0.3 0.4 0.5 0.7 0.8 Number of voters 1 4 5 6 5 6 4 -What is the median of the distribution?

Use the following information to answer the Questions Consider the following distribution of 32 voters at eight different positions over the interval [0, 1]. Location 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Number of voters 1 6 2 7 7 2 6 1 -Candidate A announces a policy position of 0.3 and Candidate B announces a policy position of 0.8. Is there a 2/3-separation opportunity for a third Candidate C to enter the race?