Topological complexity of manifolds of preferences
AbstractThe problem of endowing preferences with manifold structures emerged from discussions with Gerard Debreu in 1975 . Time has shown that such structures can be useful in understanding the behavior of economic systems . In Chichilnisky (1976) spaces of smooth preferences were endowed with a Hilbert manifold structure, and this was used to study the existence and structural stability of competitive equilibria in economies where preferences might be non-monotonic and non-convex . This paper constructs manifolds of preferences and applies this construction to the aggregation of preferences . We examine the topological complexity of manifolds of smooth preferences and use this to determine when appropriate aggregation rules exist and when they do not .
Download InfoIf 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.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 8119.
Date of creation: 1986
Date of revision:
preferences; manifold structures; debreu; economic systems; Hilbert spaces; manifold; topological; smooth preferences; aggregation; convex; monotonic; continuous; modelling; modeling; mathematical models; topology;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
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.:
- Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, Elsevier, Elsevier, vol. 15(1), pages 160-173, June.
- Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
- DEBREU, Gérard, .
CORE Discussion Papers RP, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE)
-132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
- Chichilnisky, Graciela, 2009.
"Avoiding extinction: equal treatment of the present and the future,"
Economics - The Open-Access, Open-Assessment E-Journal,
Kiel Institute for the World Economy, vol. 3(32), pages 1-25.
- Chichilnisky, Graciela, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Economics Discussion Papers 2009-8, Kiel Institute for the World Economy.
- Graciela Chichilnisky, 2009. "Avoiding Extinction: Equal Treatment of the Present and the Future," Working Papers, LAMETA, Universtiy of Montpellier 09-07, LAMETA, Universtiy of Montpellier, revised Aug 2009.
- Chichilnisky, Graciela, 1997.
"A topological invariant for competitive markets,"
Journal of Mathematical Economics,
Elsevier, vol. 28(4), pages 445-469, November.
- Chichilnisky, G., 1996. "A Topological Invariant for Competitive Markets," Discussion Papers, Columbia University, Department of Economics 1996_16, Columbia University, Department of Economics.
- Chichilnisky, Graciela, 1990. "General equilibrium and social choice with increasing returns," MPRA Paper 8124, University Library of Munich, Germany.
- Lauwers, Luc, 2000.
"Topological social choice,"
Mathematical Social Sciences, Elsevier,
Elsevier, vol. 40(1), pages 1-39, July.
- Luc Lauwers, 1999. "Topological Social Choice," Center for Economic Studies - Discussion papers, Katholieke Universiteit Leuven, Centrum voor Economische StudiÃ«n ces9912, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
- Graciela Chichilnisky, 1996.
"A robust theory of resource allocation,"
Social Choice and Welfare, Springer,
Springer, vol. 13(1), pages 1-10, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.