Approximately stable committee selection

In the committee selection problem, we are given m candidates, and n voters. Candidates can have different weights. A committee is a subset of candidates, and its weight is the sum of weights of its candidates. Each voter expresses an ordinal ranking over all possible committees. The only assumption we make on preferences is monotonicity: If S ⊆ S′ are two committees, then any voter weakly prefers S′ to S.