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Social choice and the topology of spaces of preferences

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  • Chichilnisky, Graciela

Abstract

Social choice theory is concerned with providing a rationale for social decisions when individuals have diverse opinions. Voting is an obvious way in which societies aggregate individual preferences to obtain social ones. The procedure of voting registers individual comparisons between alternatives, called ordinal preferences, rather than intensities of preferences among these alternatives, called cardinal preferences, and this is one source of so-called paradox of social choice. It is the purpose of this paper to study the paradox of social choice and to show that it arises, in part, because of the topological structure of spaces of ordinal preferences.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8006.

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Date of creation: 1980
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Publication status: Published in Advances in Mathematics no. 2.37(1980): pp. 165-176
Handle: RePEc:pra:mprapa:8006

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Related research

Keywords: preferences; social choice; individual preference; social preference; topological structure; topology; ordinal preferences; cardinal preferences;

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Citations

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Cited by:
  1. Andrea Beltratti & Graciela Chichilnisky & Geoffrey Heal, 1993. "Sustainable Growth and the Green Golden Rule," NBER Working Papers 4430, National Bureau of Economic Research, Inc.
  2. 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.
  3. Ju, Biung-Ghi, 2004. "Continuous selections from the Pareto correspondence and non-manipulability in exchange economies," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 573-592, August.
  4. Chichilnisky, Graciela, 1985. "Von Neuman- Morgenstern utilities and cardinal preferences," MPRA Paper 8090, University Library of Munich, Germany.
  5. Chichilnisky, Graciela, 1994. "A robust theory of resource allocation," MPRA Paper 8599, University Library of Munich, Germany.
  6. Lauwers, Luc, 2000. "Topological social choice," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 1-39, July.
  7. Maurice Salles, 2014. "‘Social choice and welfare’ at 30: its role in the development of social choice theory and welfare economics," Social Choice and Welfare, Springer, vol. 42(1), pages 1-16, January.
  8. Luigi Marengo & Simona Settepanella, 2010. "Social choice among complex objects," LEM Papers Series 2010/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  9. repec:ebl:ecbull:v:3:y:2005:i:4:p:1-7 is not listed on IDEAS
  10. Chichilnisky, Graciela, 1990. "On the mathematical foundations of political economy," MPRA Paper 8123, University Library of Munich, Germany.
  11. 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.
  12. Chichilnisky, Graciela, 1986. "Topological complexity of manifolds of preferences," MPRA Paper 8119, University Library of Munich, Germany.
  13. Baryshnikov, Yuliy M., 2000. "On isotopic dictators and homological manipulators," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 123-134, February.
  14. Luc Lauwers, 2002. "A note on Chichilnisky's social choice paradox," Theory and Decision, Springer, vol. 52(3), pages 261-266, May.
  15. Chichilnisky, Graciela, 1990. "General equilibrium and social choice with increasing returns," MPRA Paper 8124, University Library of Munich, Germany.
  16. Tanaka, Yasuhito, 2007. "A topological approach to Wilson's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 184-191, February.
  17. Campbell, Donald E. & Kelly, Jerry S., 1996. "Continuous-valued social choice," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 195-211.
  18. 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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