Broome on Fairness and Lotteries

John Broome argues that when all claims cannot be perfectly fairly satisfied in outcome, the contribution to fairness from entering claims into a lottery, and so providing them some surrogate satisfaction, ought to be weighed against, and can outweigh, what fairness can be achieved directly in outcome. I argue that this is a mistake. Instead, I suggest that any contribution to fairness from entering claims into a lottery is lexically posterior to fairness in outcome.