Suppose that there are two candidates, L and R, with ideologies Y_L < Y_R. Assume voters care only about the ideology of candidates. The winning candidate is the one closest to the ideology of the median voter, Ym. Specifically, the median voter votes for L if and only if Y_m < (Y_L + Y_R)/2 M

Now suppose that M is unknown, In particular, your beliefs about M are represented as follows: M~N (1, 1)

You encounter new information that is relevant to M. Suppose beliefs about how the new information relates to M is as follows:

Z = M 1 +

where is independent noise represented by a normal distribution with mean zero and variance ²

(a) Can you infer the ideological bias, if any, of the new information? Explain

(b) Suppose y_m = 0. Based on the prior, which candidate wins? Derive the probability that the wrong candidate is elected.

(c) Suppose z = 2. What is the probability that the median voter votes for candidate R? How does it depend on ² ? Provide intuition.

(d) Assume the median will turn out to vote only if he is 95% sure who to support. Derive the values of z that ensure the median abstains? Provide intuition.