Assume that people are uniformly distributed on the line from 0 to 1 in the order of their preferences. There are two candidates choosing their positions, c1 and c2, respectively, and people will vote for the candidate that is close to them.

a. Given c1 = 0, what is the optimal c2?

b. Given c1 = 0.2, what is the optimal c2?

c. Given c1 = 0.8, what is the optimal c2?

d. Given c1 = 0.5, what is the optimal c2?