  Recovering and distinguishing between the potentially meaningful indifference
and/or indecisiveness parts of a decision maker's preferences from their
observable choice behaviour is important for testing theory and conducting
welfare analysis. This paper contributes a way forward in two ways. First, it
reports on a new experimental design with a forced and a non-forced general
choice treatment where the 282 subjects in the sample were allowed to choose
*multiple* gift-card bundles from each menu they saw. Second, it analyses the
collected data with a new non-parametric combinatorial-optimization method that
allows to compare the goodness-of-fit of utility maximization to that of models
of undominated or dominant choice with incomplete preferences, in each case
with or without indifferences. Most subjects in the sample are
well-approximated by some indifference-permitting instance of those three
models. Furthermore, the model-specific preference recovery typically elicits a
unique preference relation with a non-trivial indifference part and, where
relevant, a distinct indecisiveness part. The two kinds of distinctions between
indifference and indecisiveness uncovered herein are theory-guided and
documented empirically for the first time. Our findings suggest that accounting
for the decision makers' possible indifference or inability to compare some
alternatives can increase the descriptive accuracy of theoretical models and
their empirical tests thereof, while it can also aid attempts to recover
people's stable but possibly weak or incomplete preferences.
