Economics 113 UCSD Winter 2010 Prof. Ross Starr, Mr. Troy Kravitz February 23, 25, 2010 1 Lecture Notes, February 23, 25, 2010 Social Choice Theory, Arrow Possibility TheoremBergson-Samuelson social welfare function W(u1(x1), u2(x2), …, u#H(x#H)) with 0iWu∂>∂all i. Let the allocation x* ∈RN(#H)+ maximize W subject to the usual technology constraints. Then x* is a Pareto efficient allocation. Further, suppose x**∈RN(#H)+ is a Pareto efficient allocation. Then there is a specification of W so that x** maximizes W subject to constraint. Paradox of Voting(Condorcet) Cyclic majority: Voter preferences: 1 2 3 A B C B C A C A B Majority votes A > B, B > C. Transitivity requires A > C but majority votes C > A. Conclusion: Majority voting on pairwise alternatives by rational (transitive) agents can give rise to intransitive group preferences. Is this an anomaly? Or systemic. Arrow Possibility Theorem says systemic. Arrow (Im) Possibility Theorem: We'll follow Sen's treatment. For simplicity we'll deal in strong orderings (strict preference) only X = Space of alternative choices
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