Science's priority rule rewards those who are first to make a discovery, at the expense of all other scientists working towards the same goal, no matter how close they may be to making the same discovery. I propose an explanation of the priority rule that, better than previous explanations, accounts for the distinctive features of the rule. My explanation treats the priority system, and more generally, any scheme of rewards for scientific endeavor, as a device for achieving an allocation of (...) resources among different research programs that provides as much benefit as possible to society. I show that the priority system is especially well suited to finding an efficient allocation of resources in those situations, characteristic of scientific inquiry, in which any success in an endeavor subsequent to the first success brings little additional benefit to society. (shrink)