Problems of social choice frequently take the following form. There are $n$ voters and a set $K = \{1, 2, ldots, k\}$ of objects. The voters must choose a subset of $K$. We define a class of voting schemes called voting by committees. The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and nonmanipulability on the domain of separable preferences. This result is analogous to the literature on the Groves and Clarke scheme in that it characterizes all of the nonmanipulable voting schemes on an important domain.