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Topological Social Choice

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  • Luc Lauwers

Abstract

The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the eighties. The main result in this area (known as the resolution of the topological social choice paradox) shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every number of individuals if and only if this space is contractible. Furthermore, connections between the Pareto principle, dictatorship, and manipulation were established. Recently, Baryshnikov used the topological approach to demonstrate that Arrow's impossibility theorem can be reformulated in terms of the non-contractibility of spheres. This paper discusses these results in a self-contained way, emphasizes the social choice interpretation of some topological concepts, and surveys the area of topological aggregation.

Suggested Citation

  • Luc Lauwers, 1999. "Topological Social Choice," Working Papers of Department of Economics, Leuven ces9912, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:ces9912
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Andrea Attar & Thomas Mariotti & François Salanié, 2019. "On a class of smooth preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 37-57, May.
    2. Yasuhito Tanaka, 2005. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem (forthcoming in ``Applied Mathematics and Computation''(Elsevier))," Public Economics 0506012, University Library of Munich, Germany, revised 17 Jun 2005.
    3. Kari Saukkonen, 2007. "Continuity of social choice functions with restricted coalition algebras," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 637-647, June.
    4. Tanaka, Yasuhito, 2009. "On the equivalence of the Arrow impossibility theorem and the Brouwer fixed point theorem when individual preferences are weak orders," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 241-249, March.
    5. Yasuhito Tanaka, 2005. "A topological approach to the Arrow impossibility theorem when individual preferences are weak orders (forcoming in ``Applied Mathematics and Compuation''(Elsevier))," Public Economics 0506013, University Library of Munich, Germany, revised 17 Jun 2005.
    6. repec:ebl:ecbull:v:4:y:2004:i:6:p:1-6 is not listed on IDEAS
    7. Luc Lauwers, 2009. "The topological approach to the aggregation of preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 449-476, September.
    8. Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    9. Yasuhito Tanaka, 2005. "A topological proof of Eliaz's unified theorem of social choice theory (forthcoming in "Applied Mathematics and Computation")," Public Economics 0510021, University Library of Munich, Germany, revised 26 Oct 2005.
    10. Mabrouk, Mohamed, 2006. "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality," MPRA Paper 10512, University Library of Munich, Germany.
    11. 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.
    12. Pivato, Marcus, 2008. "Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions," MPRA Paper 7461, University Library of Munich, Germany.
    13. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.
    14. 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.
    15. Daniel Eckert, 2004. "Proximity Preservation in an Anonymous Framework," Economics Bulletin, AccessEcon, vol. 4(6), pages 1-6.
    16. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.

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    21. 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.

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