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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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    1. Chichilnisky, Graciela & Heal, Geoffrey, 1984. "Patterns of power: bargaining and incentives in two-person games," Journal of Public Economics, Elsevier, vol. 23(3), pages 333-349, April.
    2. Heine Rasmussen, 1997. "Strategy-proofness of continuous aggregation maps (*)," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 249-257.
    3. Graciela Chichilnisky, 1996. "A robust theory of resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 1-10, January.
    4. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    5. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
    6. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    7. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
    8. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(1), pages 161-169.
    9. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
    10. I.D.A. Macintyre, 1998. "Two-Person and majority continuous aggregation in 2-good space in Social Choice: a note," Theory and Decision, Springer, vol. 44(2), pages 199-209, April.
    11. Donald G. Saari, 1997. "Informational geometry of social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 211-232.
    12. Geoffrey Heal, 1997. "Social choice and resource allocation: a topological perspective," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 147-160.
    13. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 295-302.
    14. Graciela Chichilnisky & Geoffrey Heal, 1997. "Social choice with infinite populations: construction of a rule and impossibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 303-318.
    15. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
    16. Maurice McManus, 1982. "Some Properties of Topological Social Choice Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 447-460.
    17. Graciela Chichilnisky, 1997. "A Unified Perspective on Resource Allocation: Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium, the Core and Social Choice," International Economic Association Series, in: Kenneth J. Arrow & Amartya Sen & Kotaro Suzumura (ed.), Social Choice Re-examined, chapter 6, pages 121-174, Palgrave Macmillan.
    18. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    19. Yuliy M. Baryshnikov, 1997. "Topological and discrete social choice: in a search of a theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 199-209.
    20. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
    21. Graciela Chichilnisky, 1993. "On Strategic Control," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 285-290.
    22. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    23. Chichilnisky, Graciela, 1997. "Limited arbitrage is necessary and sufficient for the existence of an equilibrium," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 470-479, November.
    24. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
    25. Uriarte, I. R., 1987. "Topological structure of a space of continuous preferences as a space of retractions and the aggregation problem," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 259-272, June.
    26. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 11-16, January.
    27. Nick Baigent, 1989. "Some Further Remarks on Preference Proximity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 191-193.
    28. Chichilnisky, G., 1993. "Intersecting Families of Sets and the Topology of Cones in Economics," Papers 93-17, Columbia - Graduate School of Business.
    29. Chichilnisky, Graciela, 1982. "The topological equivalence of the pareto condition and the existence of a dictator," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 223-233, March.
    30. Baigent, Nick, 1984. "A reformulation of Chichilnisky's impossibility theorem," Economics Letters, Elsevier, vol. 16(1-2), pages 23-25.
    31. Lauwers, Luc, 1993. "Infinite Chichilnisky rules," Economics Letters, Elsevier, vol. 42(4), pages 349-352.
    32. Kelly, Jerry S, 1971. "The Continuous Representation of a Social Preference Ordering," Econometrica, Econometric Society, vol. 39(3), pages 593-597, May.
    33. Luc Lauwers, 1997. "Topological aggregation, the case of an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 319-332.
    34. Campbell, Donald E, 1992. "Transitive Social Choice in Economic Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(2), pages 341-352, May.
    35. E. IndurÂin & J. C. Candeal & G. Chichilnisky, 1997. "Topological aggregation of preferences: the case of a continuum of agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 333-343.
    36. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
    37. Esteban Induráin & José Ramón Uriarte & Juan Carlos Candeal, 1997. "Some issues related to the topological aggregation of preferences: addendum (*)," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 359-361.
    38. Yuqing Zhou, 1997. "A note on continuous social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 245-248.
    39. Baigent, Nick, 1985. "Anonymity and continuous social choice," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 1-4, February.
    40. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
    41. Graciela Chichilnisky, 1996. "Actions of symmetry groups," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(3), pages 357-364.
    42. Shmuel Nitzan, 1989. "More on the Preservation of Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 187-190.
    43. Efimov, Boris A. & Koshevoy, Gleb A., 1994. "A topological approach to social choice with infinite populations," Mathematical Social Sciences, Elsevier, vol. 27(2), pages 145-157, April.
    44. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
    45. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(2), pages 233-243.
    46. Nitzan, Shmuel, 1976. "On Linear and Lexicographic Orders, Majority Rule and Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 213-219, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Pivato, Marcus, 2008. "Sustainable preferences via nondiscounted, hyperreal intergenerational welfare functions," MPRA Paper 7461, University Library of Munich, Germany.
    5. 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.
    6. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.
    7. 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.
    8. 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.
    9. 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.
    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. Daniel Eckert, 2004. "Proximity Preservation in an Anonymous Framework," Economics Bulletin, AccessEcon, vol. 4(6), pages 1-6.
    12. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.
    13. 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.
    14. Crespo, Juan A. & Sanchez-Gabites, J.J, 2016. "Solving the Social Choice problem under equality constraints," MPRA Paper 72757, University Library of Munich, Germany.
    15. 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.
    16. repec:ebl:ecbull:v:4:y:2004:i:6:p:1-6 is not listed on IDEAS

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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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