  We study the computational complexity of committee selection problem for
several approval-based voting rules in the presence of outliers. Our first
result shows that outlier consideration makes committee selection problem
intractable for approval, net approval, and minisum approval voting rules. We
then study parameterized complexity of this problem with five natural
parameters, namely the target score, the size of the committee (and its dual
parameter, the number of candidates outside the committee), the number of
outliers (and its dual parameter, the number of non-outliers). For net approval
and minisum approval voting rules, we provide a dichotomous result, resolving
the parameterized complexity of this problem for all subsets of five natural
parameters considered (by showing either FPT or W[1]-hardness for all subsets
of parameters). For the approval voting rule, we resolve the parameterized
complexity of this problem for all subsets of parameters except one.
  We also study approximation algorithms for this problem. We show that there
does not exist any alpha(.) factor approximation algorithm for approval and net
approval voting rules, for any computable function alpha(.), unless P=NP. For
the minisum voting rule, we provide a pseudopolynomial (1+eps) factor
approximation algorithm.
