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Chapter Eighteen - Topological Theories of Social Choice

In: Handbook of Social Choice and Welfare

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  • Baigent, Nicholas

Abstract

This chapter presents a simple introduction to the main results in topological social choice theory. Given a continuous social welfare function, these results show the following: (i) Unanimity and Anonymity are incompatible; (ii) Weak Pareto and No Veto are incompatible; and (iii) Weak Pareto implies the existence of a Strategic Manipulator. Given the role of continuity in all these results, its justification is critically discussed. Finally, a remarkable proof of Arrow's theorem using topological methods is presented.

Suggested Citation

  • Baigent, Nicholas, 2011. "Chapter Eighteen - Topological Theories of Social Choice," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 18, pages 301-334, Elsevier.
    • Handle: RePEc:eee:socchp:2-18
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    Cited by:

    1. Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    2. Greenfield, Mark & Zhang, Jun, 2018. "Null preference and the resolution of the topological social choice paradox," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 47-51.
    3. Guillaume Chèze, 2017. "Topological aggregation, the twin paradox and the No Show paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 707-715, April.
    4. Muto, Nozomu & Sato, Shin, 2017. "An impossibility under bounded response of social choice functions," Games and Economic Behavior, Elsevier, vol. 106(C), pages 1-15.
    5. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • I0 - Health, Education, and Welfare - - General

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