28.6* Everyday Application: Citizen Candidates: Whenever we have modeled political candidates who stand for election, we have assumed that they care only about winning and are perfectly content to change their position in whatever way maximizes the probability of winning. Now consider a different way of thinking about political candidates: Suppose that the citizens again have uniformly distributed ideal points on the Hotelling line [0,1]. Before any election is held, each citizen has to decide whether to pay the cost c . 0 to run as a candidate, with the payoff from probability p of winning the election equal to 1p 2 c2.