Randomized controlled trials, which randomly allocate benefits to a treatment group and not a control group, ascribe differences in post-treatment welfare to the benefits being allocated. However, it is possible that potential recipients' welfare is not only affected by the receipt of the program, but also by the allocation mechanism (procedural utility). In this paper, we ask whether potential recipients support or oppose random allocation of financial benefits, by allowing them to reward or punish an allocator conditional on her choice of allocation mechanism: direct allocation to one recipient vs. randomization among potential recipients. We find that when potential recipients have equal endowments, they on average reward the allocator for randomizing. When instead there is inequality in the potential recipients' endowments, the relatively poorer recipients punish allocators who randomize, while the relatively richer potential recipients neither reward nor punish the allocator for randomizing. Our results suggest that an allocator who chooses to randomize between potential recipients with unequal endowments imposes a social cost on the relatively poorer potential recipients.