Topological complexity of manifolds of preferences
The 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 .
|Date of creation:||1986|
|Publication status:||Published in Contributions to Mathematical Economics- In honor of Gerald Debreu (1986): pp. 131-142|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
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- Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, Elsevier, vol. 15(1), pages 160-173, June.
- Debreu, Gerard, 1972.
Econometric Society, vol. 40(4), pages 603-615, July.
- DEBREU, Gérard, "undated". "Smooth preferences," CORE Discussion Papers RP 132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Chichilnisky, Graciela, 1977. "Nonlinear functional analysis and optimal economic growth," MPRA Paper 7990, University Library of Munich, Germany.
- Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany. Full references (including those not matched with items on IDEAS)