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Choice functions and abstract convex geometries. (English) Zbl 0943.91031

Summary: A main aim of this paper is to make connections between two well – but up to now independently – developed theories, the theory of choice functions and the theory of closure operators. It is shown that the classes of ordinally rationalizable and path independent choice functions are related to the classes of distributive and anti-exchange closures.

MSC:

91B14 Social choice
91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in general)
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References:

[1] Aizerman, M.A., New problems in the general choice theory, Social choice and welfare, 2, 235-282, (1985) · Zbl 0583.90004
[2] Edelman, P.H. Abstract convexity and meet-distributive lattices, in: I. Rival (Ed.), Proc. AMS-IMS-SIAM Conference on Combinatorics and Ordered Sets, Arcata, 1985, Contemporary Mathematics, vol. 57, AMS, Providence, RI, 1986, pp. 127-150.
[3] Edelman, P.H.; Jamison, R., The theory of convex geometries, Geom. dedicata, 19, 247-270, (1985) · Zbl 0577.52001
[4] Gratzer, G. General Lattice Theory, Springer-Verlag, Berlin, New York, 1978. · Zbl 0385.06015
[5] Moulin, H., Choice functions over a finite set: a summary, Social choice and welfare, 2, 147-160, (1985) · Zbl 0576.90004
[6] Plott, C.R., Path independence and social choices, Econometrica, 41, 1075-1091, (1973) · Zbl 0297.90017
[7] Sen, A.K., Social choice theory: A re-examination, Econometrica, 45, 53-89, (1977) · Zbl 0353.90001
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