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 .
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- Debreu, Gerard, 1972.
Econometric Society, vol. 40(4), pages 603-15, July.
- Chichilnisky, Graciela, 1977. "Spaces of economic agents," Journal of Economic Theory, 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.
- Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
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