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Topological Social Choice

  • Luc Lauwers

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.

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Paper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces9912.

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Date of creation: Mar 1999
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Handle: RePEc:ete:ceswps:ces9912
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  1. 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 341-52, May.
  2. Chichilnisky, Graciela, 1994. "A robust theory of resource allocation," MPRA Paper 8599, University Library of Munich, Germany.
  3. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
  4. 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.
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  8. 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 213-19, February.
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  10. Geoffrey Heal, 1997. "Social choice and resource allocation: a topological perspective," Social Choice and Welfare, Springer, vol. 14(2), pages 147-160.
  11. Chichilnisky, G., 1990. "On Strategic Control," Discussion Papers 1990_30, Columbia University, Department of Economics.
  12. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
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  16. 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.
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  20. Lauwers, Luc, 1993. "Infinite Chichilnisky rules," Economics Letters, Elsevier, vol. 42(4), pages 349-352.
  21. Baigent, Nick, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, MIT Press, vol. 102(1), pages 161-69, February.
  22. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
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  24. Heine Rasmussen, 1997. "Strategy-proofness of continuous aggregation maps (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 249-257.
  25. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  26. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer, vol. 13(1), pages 11-16, January.
  27. Baigent, Nick, 1989. "Some Further Remarks on Preference Proximity," The Quarterly Journal of Economics, MIT Press, vol. 104(1), pages 191-93, February.
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  29. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
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  31. Baigent, Nick, 1985. "Anonymity and continuous social choice," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 1-4, February.
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  33. 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.
  34. Chichilnisky, G. & n, D.B. & O'Flaherty, B., 1991. "Actions of Asymmetry Groups," Discussion Papers 1991_21, Columbia University, Department of Economics.
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  37. Nitzan, Shmuel, 1989. "More on the Preservation of Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, MIT Press, vol. 104(1), pages 187-90, February.
  38. 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.
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  40. Luc Lauwers, 1997. "Topological aggregation, the case of an infinite population," Social Choice and Welfare, Springer, vol. 14(2), pages 319-332.
  41. 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.
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