Pseudo-rationalizability over Infinite Choice Spaces

A dominant concern in rational choice theory is rationalizability of choice functions. Rationalizability demands that a choice function can be represented by a preference relation according to which the choice function selects for each decision problem those alternatives which are most preferred (or undominated by other alternatives). A less demanding notion demands that a choice function can be represented by a collection of preference relations according to which for each decision problem the choice function selects those alternatives which are best (or undominated) for at least one preference relation in the given collection. This notion, called pseudo-rationalizability, has been given special attention in social choice theory and by philosophers such as Hans Rott and Isaac Levi. The purpose of this article is to extend known representation results due to Aizerman and Malishevski [1] and Moulin [5]. In [1] and [5] it is assumed that the underlying set of all optionsX is finite and the domain of the choice function consists of all finite nonempty subsets of X . We extend these results, relaxing both assumptions. Summary of Present