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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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 .
|Item Type:||MPRA Paper|
|Original Title:||Topological complexity of manifolds of preferences|
|Keywords:||preferences; manifold structures; debreu; economic systems; Hilbert spaces; manifold; topological; smooth preferences; aggregation; convex; monotonic; continuous; modelling; modeling; mathematical models; topology|
|Subjects:||C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods|
|Depositing User:||Graciela Chichilnisky|
|Date Deposited:||07. Apr 2008 01:37|
|Last Modified:||17. Feb 2013 22:33|
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