IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Social choice and the closed convergence topology

Listed author(s):
  • Chichilnisky, Graciela

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1900 a, b). Theorems 1 and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences Psco, its subspace of smooth preferences Pssco, and a space P1 of smooth (not necessarily convex) preferences with a unique interior critical point (a maximum). The results are proven using both the closed convergence topology and the smooth topology. Because of their contractibility, these spaces satisfy the necessary and sufficient conditions of Chichilnisky and Heal (1983) for aggregation rules satisfying my axioms, which are valid in all topologies. Theorem 4 constructs a family of aggregation rules satisfying my axioms for these three spaces. What these spaces have in common is a unique maximum (or peak). This rather special property makes them contractible, and thus amenable to aggregation rules satisfying anonymity and unanimity, Chichilnisky (1980 1982). The results presented here clarify an erroneous example in LeBreton and Uriarte (1990a, b) and respond to Baigent (1984, 1985, 1987) and Baigent and Huang (1990) on the relative advantages of continuous and discrete approaches to Social Choice.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: original version
Download Restriction: no

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8353.

in new window

Date of creation: 12 Jul 1990
Handle: RePEc:pra:mprapa:8353
Contact details of provider: Postal:
Ludwigstraße 33, D-80539 Munich, Germany

Phone: +49-(0)89-2180-2459
Fax: +49-(0)89-2180-992459
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  1. 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.
  2. Nick Baigent, 1989. "Some Further Remarks on Preference Proximity," The Quarterly Journal of Economics, Oxford University Press, vol. 104(1), pages 191-193.
  3. Graciela Chichilnisky, 1990. "On The Mathematical Foundations Of Political Economy," Contributions to Political Economy, Oxford University Press, vol. 9(1), pages 25-41.
  4. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
  5. Chichilnisky, Graciela, 1979. "On fixed point theorems and social choice paradoxes," Economics Letters, Elsevier, vol. 3(4), pages 347-351.
  6. Nick Baigent, 1987. "Preference Proximity and Anonymous Social Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 102(1), pages 161-169.
  7. Chichilnisky, Graciela, 1983. "Social choice and game theory: recent results with a topological approach," MPRA Paper 8059, University Library of Munich, Germany.
  8. Maurice Salles, 2005. "Social Choice," Post-Print halshs-00337075, HAL.
  9. Chichilnisky, Graciela, 1990. "General equilibrium and social choice with increasing returns," MPRA Paper 8124, University Library of Munich, Germany.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:8353. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.