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Social Choice Problem Set --- Suggested Answers

# Social Choice Problem Set --- Suggested Answers - Economics...

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Economics 113 Prof. R. Starr, Mr. Troy Kravitz UCSD Winter 2010 1 Social Choice Theory Problem Set 1. Consider majority voting over pairwise alternatives subject to agenda manipulation. Use the following voting rules and preference profiles. There are three propositions to choose among, A, B, and C. There are three voters, 1, 2, 3. The notation > indicates strict preference. Rules: There is a chairman who sets the agenda, the order of voting. He announces two propositions to choose between; the winner of that vote faces a runoff against the remaining alternative. Profile I: Voter 1: A > B > C Voter 2: B > C > A Voter 3: C > A > B Profile II: Voter 1: A > B > C Voter 2: B > C, B > A, (C vs. A preference is unspecified) Voter 3: C > B > A Claim: Under Profile I the chair can arrange that any one of the three propositions be the winner by the chair’s choice of the order of voting. Under Profile II, the choice is independent of the order of the agenda. (a) Demonstrate the claim. (b) Show that Profile II fulfills the concept of “single peaked preferences” and that Profile I does not. Suggested Answer: (a) Profile I: Chair says primary is A vs. B; A wins primary; C wins runoff Chair says primary is B vs. C; B wins primary; A wins runoff Chair says primary is A vs. C; C wins primary; B wins runoff Profile II: Chair says primary is A vs. B; B wins primary; B wins runoff Chair says primary is B vs. C; B wins primary; B wins runoff Chair says primary is A vs. C; voter 2’s choice of A or C wins primary; B wins runoff (b) Assume a left to right ordering A, B, C. Profile 2 is single peaked; voter 1’s peak is A, voter 2’s peak is B, voter 3’s peak is C.

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Social Choice Problem Set --- Suggested Answers - Economics...

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