Numerical representations of choice functions allow the expression of a problem of choice as a problem of finding maxima of real valued functions, which requires less information to be defined and which is easier to work with. In this paper, the existence of numerical representations of choice functions by imposing assumptions directly on the choice function, is obtained. In particular, it is proved that (IIA) is a necessary and sufficient condition for a choice function to be representable, if the set of alternatives is countable, while the conjunction of (IIA) and a continuity condition is sufficient to ensure it in separable topological spaces.
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Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number
1998-01.