Team Performance with Test Scores

Team performance is a ubiquitous area of inquiry in the social sciences, and it motivates the problem of team selection -- choosing the members of a team for maximum performance. Influential work of Hong and Page has argued that testing individuals in isolation and then assembling the highest-scoring ones into a team is not an effective method for team selection. For a broad class of performance measures, based on the expected maximum of random variables representing individual candidates, we show that tests directly measuring individual performance are indeed ineffective, but that a more subtle family of tests used in isolation can provide a constant-factor approximation for team performance. These new tests measure the "potential" of individuals, in a precise sense, rather than performance; to our knowledge they represent the first time that individual tests have been shown to produce near-optimal teams for a non-trivial team performance measure. We also show families of subdmodular and supermodular team performance functions for which no test applied to individuals can produce near-optimal teams, and discuss implications for submodular maximization via hill-climbing.