Meritocratic systems are commonly understood as those that assign tasks to individuals who can best perform them. But future performance cannot be known prior to assignment, and must be inferred from other traits. We consider a model in which performance depends on two attributes —- ability and training —- where ability is endowed and unobserved and training is acquired and observed. The potential to acquire training depends on ability and resource access, so ability affects performance through two channels: indirectly through training and directly through the performance function. The population consists of two identity groups, each with the same ability distribution, but with differential access to resources. We characterize the sets of training levels that maximize expected performance. An allocation is monotonic if, for each group, there is a threshold value of training such that all those above this value (and none below) are selected. It is group-blind if assignment is independent of group identity, and psuedomeritocratic if it is both monotonic and group-blind. We show that performance-maximizing allocations are not generally monotonic or group-blind, and are pseudomeritocratic under only very special conditions. This is true even when individuals can respond to non-monotonic policies by underinvesting in training, or when commitment to selection policies is possible.

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