Consider two political candidates A and B facing an electorate with ideologicalpositions uniformly distributed between 0 and 1. (To remind you, uniformly distributedmeans there are equal numbers of voters in the interval between 0.4 and 0.6 as between0.8 and 1.0 and any interval of the same length.) Candidates want to maximize their voteshares. Each simultaneously and independently of the other announces a position betweenO and 1. A voter chooses to vote for a candidate who is closest to her but will abstain ratherthan 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.

Nash equilibrium is a concept that is used in Game theory mainly. It is used to determine the…

Answered: Consider two political candidates A and…

Macroeconomics

13th Edition

ISBN:9781337617390

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter19: Public Choice And Special Interest Group Politics

Section: Chapter Questions

Problem 1WNG

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Match the following according to the criterion. If a candidate receives [ Choose ] more than half the first- place votes in an election, then that candidate should be declared the winner. If a candidate is favored [ Choose ] when compared separately with every other candidate in an election, then that candidate should be declared the winner. If a candidate wins an [ Choose] election and, in a reelection, the only changes are changes that favor the candidate, then that candidate should win the reelection. If a candidate wins an [ Choose ] election and, in a recount, the only changes are that one or more of the other candidates are removed from the ballot, then that candidate should still win the election.
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?…
- = 1.8. Consider a population of voters uniformly distributed along the ideological spectrum from left (x = 0) to right (x = 1). Each of the candidates for a single office simultaneously chooses a cam- paign platform (i.e., a point on the line between x 0 and x 1). The voters observe the candidates' choices, and then each voter votes for the candidate whose platform is closest to the voter's position on the spectrum. If there are two candidates and they choose platforms x₁ = .3 and x2 = .6, for example, then all voters to the left of x .45 vote for candidate 1, all those to the right vote for candidate 2, and candidate 2 wins the elec- tion with 55 percent of the vote. Suppose that the candidates care only about being elected—they do not really care about their platforms at all! If there are two candidates, what is the pure- strategy Nash equilibrium? If there are three candidates, exhibit a pure-strategy Nash equilibrium. (Assume that any candidates who choose the same platform…
Problem 2. The planning committee for a renewable energy trade show is trying to decide what city to hold their next show in. The votes are shown below. Numbers of Voters 9 19 11 8 1st choice Buffalo Atlanta Chicago Buffalo 2nd choice Atlanta Buffalo Buffalo Chicago 3rd choice Chicago Chicago Atlanta Atlanta How many voters voted in this election? How many votes are needed for a majority? A plurality? Find the winner under the plurality method. Find the winner under the Borda Count Method. Find the winner under the Plurality with Elimination method. Find the winner under the Pairwise Comparison Voting method.
Each one has ONE Senator who votes for their state and is elected only by the voters in their own state. Each Senator's vote is equal in the voting process. There are three projects being considered and each will only bring revenue into the one State in which it is built BUT all three projects, if built, will be built with Taxes paid by ALL of the population of all 5 states. District 1 is not considering a project at this time. District 2 is mostly urban and they want to build a Football stadium to attract tourists. District 3 is not considering a project at this time. District 4 wants to build a Space Exploration Research Center. District 5 wants to build an airport. The relevant Benefit (positive number) and Cost (negative number) to each district details are below: District I District II District III District IV District V O Regulatory Capture Logrolling Stadium ($) -30 80 -30 -30 -30 The Scenario outlined above is commonly known as: Kleptocracy Rent Seeking Airport ($) -25 -25 -25…
Does traditional one-person-one-vote (1p1v) majority voting allow voters to directly express differences in strengths of preference? Does quadratic voting do any better? Discuss the differences and then explain which system you prefer, and why.
Assume there are three voters: A, B and C. Voter preferences can be ranked along a left-to-right spectrum that ranges from 1-9; 1 being the most left leaning preference and 9 being the most right leaning preference. Suppose these voters will choose between candidates Smith and Jones in an upcoming election. Assuming the following voter preferences: True/False Explain: If the median voter theorem holds, candidates Smith and Jones will either both adopt preference 5 OR one will adopt preference 4 while the other adopts preference 6. B. Suppose the electorate becomes more polarized; A moves from 4 to 1 while C moves from 6 to 9. B remains at 4. How does the median voter model predict candidates Smith and Jones will change their preference? C. Keeping the assumptions from B, how does the election result change if a tax on non-voters doubles the number of voters while preserving the distribution of preferences? D. If the tax in C induces 100% compliance (everyone votes), did this tax…
Bella Robinson and Steve Carson are running for a seat in the U.S. Senate. If both candidates campaign only in the major cities of the state, then Robinson is expected to get 80% of the votes; if both candidates campaign in only rural areas, then Robinson is expected get 75% of the votes; if Robinson campaigns exclusively in the city and Carson campaigns exclusively in the rural areas, then Robinson is expected to get 30% of the votes; finally, if Robinson campaigns exclusively in the rural areas and Carson campaigns exclusively in the city, then Robinson is expected to get 65% of the votes. (a) Construct the payoff matrix for the game. (Enter each percentage as a decimal.) Carson City Rural Robinson CityRural Is the game strictly determined? YesNo (b) Find the optimal strategy for both Robinson (row) and Carson (column). P = Q =
Suppose that friends Jennifer, Stephanie, and Megan cannot agree on how much to spend for a bouquet of flowers to send to a person who allowed them to use her beach house for the weekend. Jennifer wants to buy a moderately priced bouquet, Stephanie wants to buy an expensive bouquet, and Megan wants to buy a very expensive bouquet. Assuming no paradox of voting, majority voting will result in the decision to buy Multiple Choice an inexpensive bouquet. a very expensive bouquet. a moderately priced bouquet. an expensive bouquet. B
4.10. A social choice function satisfies the weak Pareto criterion if,whenever every voter places one candidate above another, say rankingcandidate A over candidate B, then candidate B cannot be the uniquewinner. (This differs from the Pareto property owing to the words “theunique”.)(a) Explain why any method that satisfies Pareto also satisfies weakPareto.(b) Explain why the antiplurality method satisfies weak Pareto.(c) Explain why the agenda method violates weak Pareto.
Answer to Part CAssume there are three voters: A, B and C. Voter preferences can be ranked along a left-to-right spectrum that ranges from 1-9; 1 being the most left leaning preference and 9 being the most right leaning preference. Suppose these voters will choose between candidates Smith and Jonesin an upcoming election.Assuming the following voter preferences:Voter ID Preference (1-9)A 4B 5C 6B. Suppose the electorate becomes more polarized; A moves from 4 to 1 while C moves from 6 to 9. B remains at 5. How does the median voter model predict candidates Smith and Jones will change their preference? C. Keeping the assumptions from B, how does the election result change if a tax on non-voters doubles the number of voters while preserving the distribution of preferences?

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