LN022310

LN022310 - Economics 113 Winter 2010 UCSD Prof. Ross Starr,...

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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 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. For simplicity we'll deal in strong orderings (strict preference) only X = Space of alternative choices
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Economics 113 UCSD Winter 2010 Prof. Ross Starr, Mr. Troy Kravitz February 23, 25, 2010 2 Π = Space of transitive strict orderings on X H = Set of voters, numbered #H Π #H = #H - fold Cartesian product of Π , space of preference profiles f: Π #H → Π , f is an Arrow Social Welfare Function. P i represents the preference ordering of typical household i. {P i } represents a preference profile, {P i } Π #H . P represents the resulting group (social) ordering. " x P
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This note was uploaded on 09/30/2011 for the course ECON 113 taught by Professor Starr,r during the Fall '08 term at UCSD.

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LN022310 - Economics 113 Winter 2010 UCSD Prof. Ross Starr,...

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