  Motivated by applications such as college admission and insurance rate
determination, we propose an evaluation problem where the inputs are controlled
by strategic individuals who can modify their features at a cost. A learner can
only partially observe the features, and aims to classify individuals with
respect to a quality score. The goal is to design an evaluation mechanism that
maximizes the overall quality score, i.e., welfare, in the population, taking
any strategic updating into account. We further study the algorithmic aspect of
finding the welfare maximizing evaluation mechanism under two specific settings
in our model. When scores are linear and mechanisms use linear scoring rules on
the observable features, we show that the optimal evaluation mechanism is an
appropriate projection of the quality score. When mechanisms must use linear
thresholds, we design a polynomial time algorithm with a (1/4)-approximation
guarantee when the underlying feature distribution is sufficiently smooth and
admits an oracle for finding dense regions. We extend our results to settings
where the prior distribution is unknown and must be learned from samples.
