Macroeconomics
Macroeconomics
13th Edition
ISBN: 9781337617390
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter 19, Problem 3WNG
To determine

Probability of winning in election.

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Consider the race for governor of a small state. The population of the state is evenly divided between three cities-Riverville, Hanover, and Danbury. The governor's race is between Ron Ruskin (the mayor of Riverville) and Ted Topple (the mayor of Hanover). Assume that no matter what is said during the campaign, Ruskin can count on the support of 100% of the Riverville population, and Topple can count on the support of 100% of the Hanover population. Assume 100% voter participation. According to the result of majority-rule voting, the next governor will be the one preferred by the majority of the residents of The two candidates are asked in a debate about their support of recreational subsidies. Public opinion polls in the city you just identified have shown the following about the level of recreational subsidies desired: • 70% want a low level 20% want a medium level • 10% want a high level Assuming that voters prefer outcomes closer to their preferred choices to outcomes further away,…
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?…
Consider two political candidates A and B facing an electorate with ideological positions uniformly distributed between 0 and 1. (To remind you, uniformly distributed means there are equal numbers of voters in the interval between 0.4 and 0.6 as between 0.8 and 1.0 and any interval of the same length.) Candidates want to maximize their vote shares. Each simultaneously and independently of the other announces a position between O and 1. A voter chooses to vote for a candidate who is closest to her but will abstain rather than vote for a candidate whose announced position is more than 0.20 distance away. Is there a Nash equilibrium in pure strategies? Explain your answer.
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