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LN052311

# LN052311 - Economics 113 Spring 2011 UCSD Prof Ross Starr...

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Economics 113 UCSD Spring 2011 Prof. Ross Starr, Ms. S. Fried May 23, 2011 1 Lecture Notes, May 23, 2011 Social Choice Theory, Arrow Possibility Theorem Bergson-Samuelson social welfare function W(u 1 (x 1 ), u 2 (x 2 ), …, u #H (x #H )) with 0 i W u all i . Let the allocation x* R N(#H) + maximize W subject to the usual technology constraints. Then x* is a Pareto efficient allocation. Further, suppose x** R N(#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 from the Handbook of Mathematical Economics as amended by his paper ARROW AND THE IMPOSSIBILITY THEOREM . For simplicity we'll deal in strong orderings (strict preference) only.

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Economics 113 UCSD Spring 2011 Prof. Ross Starr, Ms. S. Fried May 23, 2011 2 X = Space of alternative choices Space of transitive strict orderings on X H = Set of voters, numbered #H #H = #H - fold Cartesian product of space of preference profiles f: #H f is an Arrow Social Welfare Function.
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