We study a model where a group of representatives is elected to make a series of decisions on behalf of voters. The quality of such a representative committee is judged based on the extent to which the decisions it makes are consistent with the voters' preferences. We assume the set of issues on which the committee will make the decisions is unknown---a committee is elected based on the preferences of the voters over the candidates, which only reflect how similar are the preferences of the voters and candidates regarding the issues. In this model we theoretically and experimentally assess qualities of various multiwinner election rules.