Stability versus rationality in choice functions

If we analyze the notion of stability (von Neumann and Morgenstern, 1944) it seems a desirable property to be fulfilled by any choice function. Paradoxically, the usual Condorcet choice functions (maximal set, top cycle, uncovered set, minimal covering, ...) are not stable in the VNM sense. In this study, we show the relationship between stability and rational choice functions, and propose an alternative notion of stability (wich we call c-stability) that solves this incompatibility problem. This new notion is closely related to the admissible set defined in Kalai and Schmeidler (1977).