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Topological social choice

  • Lauwers, Luc

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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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 40 (2000)
Issue (Month): 1 (July)
Pages: 1-39

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Handle: RePEc:eee:matsoc:v:40:y:2000:i:1:p:1-39
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Shmuel Nitzan, 1989. "More on the Preservation of Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 104(1), pages 187-190.
  2. Chichilnisky, Graciela, 1994. "A robust theory of resource allocation," MPRA Paper 8599, University Library of Munich, Germany.
  3. Yuqing Zhou, 1997. "A note on continuous social choice," Social Choice and Welfare, Springer, vol. 14(2), pages 245-248.
  4. Beth Allen, 1996. "A remark on a social choice problem," Social Choice and Welfare, Springer, vol. 13(1), pages 11-16, January.
  5. Yuliy M. Baryshnikov, 1997. "Topological and discrete social choice: in a search of a theory," Social Choice and Welfare, Springer, vol. 14(2), pages 199-209.
  6. Gleb Koshevoy, 1997. "Homotopy properties of Pareto aggregation rules," Social Choice and Welfare, Springer, vol. 14(2), pages 295-302.
  7. Graciela Chichilnisky, 1993. "On Strategic Control," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 285-290.
  8. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
  9. E. IndurÂin & J. C. Candeal & G. Chichilnisky, 1997. "Topological aggregation of preferences: the case of a continuum of agents," Social Choice and Welfare, Springer, vol. 14(2), pages 333-343.
  10. Nick Baigent, 1989. "Some Further Remarks on Preference Proximity," The Quarterly Journal of Economics, Oxford University Press, vol. 104(1), pages 191-193.
  11. Luc Lauwers, 1997. "Topological aggregation, the case of an infinite population," Social Choice and Welfare, Springer, vol. 14(2), pages 319-332.
  12. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
  13. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, Oxford University Press, vol. 97(2), pages 337-352.
  14. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP 132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Lauwers, Luc, 1993. "Infinite Chichilnisky rules," Economics Letters, Elsevier, vol. 42(4), pages 349-352.
  16. Wilson, Robert, 1972. "Social choice theory without the Pareto Principle," Journal of Economic Theory, Elsevier, vol. 5(3), pages 478-486, December.
  17. 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.
  18. 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.
  19. Heal, G.M., 1995. "Social Choice and Resource Allocation: A Topological Perspective," Papers 95-18, Columbia - Graduate School of Business.
  20. Baigent, Nick, 1985. "Anonymity and continuous social choice," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 1-4, February.
  21. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
  22. 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.
  23. 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.
  24. 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.
  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. Heine Rasmussen, 1997. "Strategy-proofness of continuous aggregation maps (*)," Social Choice and Welfare, Springer, vol. 14(2), pages 249-257.
  27. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
  28. 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.
  29. Donald G. Saari, 1997. "Informational geometry of social choice," Social Choice and Welfare, Springer, vol. 14(2), pages 211-232.
  30. Candeal, Juan Carlos & Indurain, Esteban, 1994. "The Moebius strip and a social choice paradox," Economics Letters, Elsevier, vol. 45(3), pages 407-412.
  31. Kelly, Jerry S, 1971. "The Continuous Representation of a Social Preference Ordering," Econometrica, Econometric Society, vol. 39(3), pages 593-97, May.
  32. Maurice McManus, 1982. "Some Properties of Topological Social Choice Functions," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 447-460.
  33. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
  34. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 102(1), pages 161-169.
  35. Paras Mehta, 1997. "Topological methods in social choice: an overview," Social Choice and Welfare, Springer, vol. 14(2), pages 233-243.
  36. Chichilnisky, G., 1993. "Intersecting Families of Sets and the Topology of Cones in Economics," Papers 93-17, Columbia - Graduate School of Business.
  37. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
  38. Graciela Chichilnisky, 1996. "Actions of symmetry groups," Social Choice and Welfare, Springer, vol. 13(3), pages 357-364.
  39. Chichilnisky, Graciela, 1982. "Structural instability of decisive majority rules," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 207-221, January.
  40. 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.
  41. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
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