Chichilnisky, Graciela (1986): Topological complexity of manifolds of preferences. Published in: Contributions to Mathematical Economics In honor of Gerald Debreu (1986): pp. 131142.

PDF
MPRA_paper_8119.pdf Download (2MB)  Preview 
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 nonmonotonic and nonconvex . 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 
Language:  English 
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 
Item ID:  8119 
Depositing User:  Graciela Chichilnisky 
Date Deposited:  07 Apr 2008 01:37 
Last Modified:  27 Sep 2019 17:54 
References:  R. Abraham and J. Robbin, "Transversal Mappings and Flows," Benjamin, New York, 1967. G. CHICHILNISKY, "Manifolds of preferences and equilibria," Technical Report No. 29, Project on Efficiency of Decision Making in Economic Systems, Harvard Univ, 1976. CHICHILNISKY, G., (1977), "Spaces of Economic Agents", Journal of Economic Theory, 16 (1), 160173. G. CHICHILNISKY, Nonlinear analysis and optimal economic growth, J. Math. Anal. and App., (1977). Chichilnisky, G . (Jan. 1980) "Social Choice and the Topology of Spaces of Preferences", Advances in Mathematics. 27, 1932. Chichilnisky, G . (1981) "Continuous Representation of Preferences", Review of Economic Studies Chichilnisky, G . and G . Heal (1983) "Necessary and Sufficient Conditions for a Resolution of the Social Choice Paradox", Journal of Economic Theory. G. DEBREU, Smooth preferences, Econometrica (1972). Debreu, G., 1964, Representation of a preference ordering by a numerical function, International Economic Review. M. W. HIRSCH, "Differential Topology," Springerverlag, New York/Heidelberg/Berlin, 1976. Hirsch, M. and B. Mazur, 1974, Smoothings of Piecewise Linear Manifolds, Annals of Mathematical Studies (Princeton University Press, Princeton, NJ) . Skorohod, A.V ., 1974, Integration in Hilbert Space (SpringerVerlag, New York) . Milnor, J ., 1965, Topology from the Differentiable Viewpoint (The University Press of Virginia, Charlottesville, VA) . S. L. SOBOLEV, "Applications of Functional Analysis in Mathematical Physics," Translations of Mathematical Monographs, America Mathematics Society, Providence, R. I., 1963. Spanier, E . (1966) Algebraic Topology (McGrawHill, New York) . 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/8119 