Recent discussion in the public sphere has explored some of the way in which prediction algorithms trained on data might exhibit bias in their decision-making. This discussion, drawing on input from a wide range of communities, has involved a number of crucial trade-offs that can be formulated in precise terms. We will survey some of these trade-offs, including tensions between the simplicity of a classification rule and its equity guarantees, and tensions between competing definitions of what it means for a prediction algorithm to be fair to different groups. The talk will be based on joint work with Jens Ludwig, Sendhil Mullainathan, Manish Raghavan, and Cass Sunstein.