  Selecting a set of alternatives based on the preferences of agents is an
important problem in committee selection and beyond. Among the various criteria
put forth for the desirability of a committee, Pareto optimality is a minimal
and important requirement. As asking agents to specify their preferences over
exponentially many subsets of alternatives is practically infeasible, we assume
that each agent specifies a weak order on single alternatives, from which a
preference relation over subsets is derived using some preference extension. We
consider five prominent extensions (responsive, downward lexicographic, upward
lexicographic, best, and worst). For each of them, we consider the
corresponding Pareto optimality notion, and we study the complexity of
computing and verifying Pareto optimal outcomes. We also consider strategic
issues: for four of the set extensions, we present a linear-time, Pareto
optimal and strategyproof algorithm that even works for weak preferences.
