  Given information about which options a decision-maker definitely rejects
from given finite sets of options, we study the implications for
decision-making with E-admissibility. This means that from any finite set of
options, we reject those options that no probability mass function compatible
with the given information gives the highest expected utility. We use the
mathematical framework of choice functions to specify choices and rejections,
and specify the available information in the form of conditions on such
functions. We characterise the most conservative extension of the given
information to a choice function that makes choices based on E-admissibility,
and provide an algorithm that computes this extension by solving linear
feasibility problems.
