Calculate simple majority voting with consistent and inconsistent efficiency.

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Chapter 31, Problem 8QP

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Calculate simple majority voting with consistent and inconsistent efficiency.

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Outline the median voter theorem and explain its importance to the successful application of a majority voting system.

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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 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?…