  Algorithm designers increasingly optimize not only for accuracy, but also for
the fairness of the algorithm across pre-defined groups. We study the tradeoff
between fairness and accuracy for any given set of inputs to the algorithm. We
propose and characterize a fairness-accuracy frontier, which consists of the
optimal points across a broad range of preferences over fairness and accuracy.
Our results identify a simple property of the inputs, group-balance, which
qualitatively determines the shape of the frontier. We further study an
information-design problem where the designer flexibly regulates the inputs
(e.g., by coarsening an input or banning its use) but the algorithm is chosen
by another agent. Whether it is optimal to ban an input generally depends on
the designer's preferences. But when inputs are group-balanced, then excluding
group identity is strictly suboptimal for all designers, and when the designer
has access to group identity, then it is strictly suboptimal to exclude any
informative input.
