Bundle: Macroeconomics, 13th + Aplia, 1 Term Printed Access Card
13th Edition
ISBN: 9781337742375
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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Arrow's impossibility theorem states that under certain assumptions about preferences, no voting system exists that satisfies all of the following properties:
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Unanimity
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Transitivity
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Independence of irrelevant alternatives
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No dictators
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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?…
Chapter 19 Solutions
Bundle: Macroeconomics, 13th + Aplia, 1 Term Printed Access Card
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- Why do we have candidate-centered elections (rather than party-centered elections) in the United States? single-member districts the Electoral College the Australian ballot independent expenditures all of the above none of the abovearrow_forwardin a voting, When a state does not win a representative to another state, though its population is increasing at a quicker rate than that of the other state. what type of paradox is thatarrow_forwardPolitical Economy 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. Voter Id Preference(1-9) A 4 B 5 C 6 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. 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? 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? If the tax in C induces 100%…arrow_forward
- Political Economy 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. Voter Id Preference(1-9) A 4 B 5 C 6 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. 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? 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? If the tax in C induces 100%…arrow_forwardPolitical Economy 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. Voter Id Preference(1-9) A 4 B 5 C 6 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 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? D) If the tax in C induces…arrow_forwardLet's walk through the median voter theorem in a little more detail. Consider a town with three voters, Enrique, Nandini, and Torsten. The big issue in the upcoming election is how high the sales tax rate should be. As you'll learn in macroeconomics (and in real life), on average, a government that wants to do more spending has to bring in more taxes, so "higher permanent taxes" is the same as "higher government spending." Enrique wants low taxes and small government, Nandini is in the middle, and Torsten wants the biggest town government of the three. Each one is a stubborn person, and his or her favorite position-what economic theorists call the "ideal point-never changes in this problem. Their preferences can be summed up like this, with the x denoting each person's favorite tax rate: Enrique 0% N O Sales tax rate Nandini P Torsten 20% Suppose there are two politicians running for office, N and O (so ignore P for now). Enrique will vote for Choose your answer. Nandini will vote for…arrow_forward
- Germany and the US are both presidential systems. Group of answer choices True Falsearrow_forwardExplain how affirmative and negative majority votes can sometimes lead to inefficient allocations of resources to public goods. Is this problem likely to be greater under a benefits-received or under an ability-to-pay tax system? Use the information in Figures 17.1a and 17.1b to show how society might be better off if Adams were allowed to buy votes.arrow_forwardWhich of the following is true? a. Arrow’s Impossibility Theorem states that There is no voting method that will satisfy a reasonable set of fairness criteria when there are three or candidates. b. Gibbard-Satterthwaite's theorem states that there is a voting method is completely resistant to strategic voting. c. None of the given choices d. May's Theorem states that the majority method will always have a winner.arrow_forward
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