1. In a congressional district somewhere in the U.S., a new representative is being elected. The voters all have one-dim

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1 In A Congressional District Somewhere In The U S A New Representative Is Being Elected The Voters All Have One Dim 1 (138.51 KiB) Viewed 40 times

1. In a congressional district somewhere in the U.S., a new representative is being elected. The voters all have one-dimensional political views that can be neatly arrayed on a left-right spectrum. We can define the "location” of a citizen's political views in the following way. The citizen with the most extreme left-wing views is said to be at point 0 and the citizen with the most extreme right-wing views is said to be at point 1. If a citizen has views that are to the right of the views of the fraction x of the state's population, that citizen's views are said to be located at point x. There are two candidates for the congressional seat and they are forced to publicly state their own political position simultaneously on the zero-one left-right scale. 1.a (2 points) Suppose voters always vote for the candidate whose stated position is nearest to their own views and suppose each candidate cares only about getting as many votes as possible. In equilibrium, what will be the two candidates' positions? 1.b (4 points) Now suppose the two candidates do not care about the number of votes that they get but only about the amount of campaign contributions that they receive. Therefore each candidate chooses his ideological location in such a way as to maximize the amount of campaign contributions he receives, given the position of the other.