In the binary voting model with two alternatives, dictatorship of voter 1 (D1) is a rule that makes the winner the first choice of voter 1, or that returns a tie when voter 1 is indifferent between x and y. D1 violates:

In the binary voting model with two alternatives, dictatorship of voter 1 (D1) is a rule that makes the winner the first choice of voter 1, or that returns a tie when voter 1 is indifferent between x and y. D1 violates:

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter16: Public Goods And Public Choice

Section: Chapter Questions

Problem 3QFR

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1.17. Jones and Smith are running for public office. There are 99 voters.(a) Suppose the rules say that Jones wins if she receives 50 or morevotes; otherwise Smith wins. Is this method neutral?(b) Suppose the rules say that a candidate wins if he or she receivesa number of votes that is between 60 and 89. (If neither candidategets a winning number of votes, then the election is a tie.) Is thismethod monotone?(c) Suppose the rules say that a candidate wins if he or she receives anodd number of votes. (If neither candidate gets a winning numberof votes, then the election is a tie.) Is this method decisive?(d) Suppose that the rules say that Smith wins the election no matterwhat. Is this method anonymous?
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Election is taking place in a city. There are two candidates, Land R. There are 100 voters numbered 1 to 100. Of them, 1 to 60 prefer candidate R, while 61 to 100 prefer candidate L. Voters know all of these things-the number of voters preferring L and R, and their own preference. Every voter receives a payoff of 1 if their preferred candidate wins and 0 otherwise. Winner is the candidate who wins the highest number votes. Voting is costly, and a voter incurs a cost of 18 to go to the booth and wait. In case of a tie, each candidate is chosen with a probability 12. Which of the following is/are true? (a) In every pure strategy Nash equilibrium, R wins with a positive probability. (b) There is a pure strategy Nash equilibrium in which L wins with a positive probability. (c) There is a pure strategy Nash Equilibrium in which every R - preferring voter goes to vote. (d) There is a pure strategy Nash Equilibrium in which exactly 2 voters go to vote and the winner is L. (e) There is no pure…
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The city council is to decide on a proposal to raise property taxes. Suppose Ms. Tuttle is the chair and the council’s other two members are Mr. Jones and Mrs. Doubtfire. The voting procedure works as follows: Excluding the chair, Mr. Jones and Mrs. Doubtfire simultaneously write down their votes on slips of paper. Each writes either for or against the tax increase. The secretary of the city council then opens the slips of paper and announces the vote tally. If the secretary reports that both slips say for, then the tax increase is implemented and the game is over. If both vote against, then the tax increase is not implemented and, again, the game is over. However, if it is reported that the vote is one for and one against, then Ms. Tuttle has to vote. If she votes for, then the tax increase is implemented, and if she votes against, then it is not. In both cases, the game is then over. As to payoffs, if the tax increase is implemented, then Mrs. Doubtfire and Mr. Jones each receive a…
- = 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…