Order extensions, budget correspondences, and rational choice

Order extensions, budget correspondences, and rational choice

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Article ID: iaor2012954
Volume: 72
Issue: 4
Start Page Number: 431
End Page Number: 444
Publication Date: Apr 2012
Journal: Theory and Decision
Authors:
Keywords: sets
Abstract:

This article is concerned with extensions of a continuous ordering R on a set X to a subset P(X) of the power set of X. The underlying topology will be the Hausdorff metric topology. We will see that continuous extensions of R do not require that P(X) contain every nonempty finite subset of X. Therefore, the analysis can be applied to consumer theory and inverse choice functions. In analogy to these functions budget correspondences are established which relate alternatives x with certain subsets of X, according to the extended ordering.

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