Topological complexity of manifolds of preferences

Graciela Chichilnisky

MPRA Paper from University Library of Munich, Germany

Abstract: 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 .

Keywords: preferences; manifold structures; debreu; economic systems; Hilbert spaces; manifold; topological; smooth preferences; aggregation; convex; monotonic; continuous; modelling; modeling; mathematical models; topology (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 1986
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Citations: View citations in EconPapers (7)

Published in Contributions to Mathematical Economics- In honor of Gerald Debreu (1986): pp. 131-142

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