  Decisions under uncertainty or with multiple objectives usually require the
decision maker to formulate a preference regarding risks or trade-offs. If this
preference is known, the ordered weighted averaging (OWA) criterion can be
applied to aggregate scenarios or objectives into a single function.
Formulating this preference, however, can be challenging, as we need to make
explicit what is usually only implicit knowledge. We explore an
optimization-based method of preference elicitation to identify appropriate OWA
weights. We follow a data-driven approach, assuming the existence of
observations, where the decision maker has chosen the preferred solution, but
otherwise remains passive during the elicitation process. We then use these
observations to determine the underlying preference by finding the preference
vector that is at minimum distance to the polyhedra of feasible vectors for
each of the observations. Using our optimization-based model, weights are
determined by solving an alternating sequence of linear programs and standard
OWA problems. Numerical experiments on risk-averse preference vectors for
selection, assignment and knapsack problems show that our passive elicitation
method compares well against having to conduct pairwise comparisons and
performs particularly well when there are inconsistencies in the decision
maker's choices.
