Principles of Microeconomics, SME 2031 Babson College
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Chapter 5.A, Problem 3ARQ
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Is the given statement is true or falls, why?
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4.12. A social choice function satisfies the bottom criterion if, whenever a candidate is not at the bottom of the preference list of any voter,that candidate is a winner.(a) Does the plurality method satisfy the bottom criterion?(b) Does the antiplurality method satisfy the bottom criterion?(c) Explain why it is impossible for a social choice function with three ormore candidates to satisfy both the bottom criterion and the Paretocriterion.
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Principles of Microeconomics, SME 2031 Babson College
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- (Last Word) The combined cost of Social Security and Medicare programs was what percent of U.S. GDP in 2008 (A) 7.6 (B) 12.4 (C) 17.2 (D) 2.9arrow_forward4.1. The vote-for-two method works as follows: Candidates get apoint whenever a voter ranks them first or second. The candidate withthe most points is declared to be the winner (or if several candidates tiefor the most points, they are all declared to be winners).(a) Does the vote-for-two method satisfy the Condorcet criterion?(b) Does the vote-for-two method satisfy the anti-Condorcet criterion?(c) Does the vote-for-two method satisfy the Pareto property?(d) Is the vote-for-two method independent?arrow_forward1.14. Consider a variation on the idea of a weighted voting system, inwhich one or more voters is given a negative weight. Show that sucha system is not monotone. If a voter knows that the method assigns anegative weight to her vote, how will she be inclined to cast her ballot?arrow_forward
- Explain 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_forward2.9. The following informal descriptions of voting methods do not represent social choice functions as we have defined them. Explain why not.(a) (Mini-quota) Any candidate with at least 25% of the votes is declareda winner.(b) (Approval voting) Every voter answers a yes-or-no question abouteach candidate: “Is she acceptable?” Whichever candidate is acceptable to the most voters is declared the winner.(c) (Copeland without ties) The winners of the Copeland method become our finalists. If there is more than one finalist, the tie is resolvedby drawing straws.(d) (Condorcet candidate) Pick the candidate who defeats each of theother candidates in a head-to-head electionarrow_forward2) What is straight-ticket voting? How does this help candidates in down ballot races?arrow_forward
- 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.arrow_forwardDoes 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.arrow_forwardAssume 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…arrow_forward
- 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?arrow_forwardHow can pork-barrel spending occur in a situation of majority voting when it benefits only a small group?arrow_forwardAnswer to Part BAssume 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?arrow_forward
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