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Topological complexity of manifolds of preferences

Chichilnisky, Graciela (1986): Topological complexity of manifolds of preferences. Published in: Contributions to Mathematical Economics- In honor of Gerald Debreu (1986): pp. 131-142.

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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 .

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