{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern