We study revealed preferences towards the use of random procedures in allocation mechanisms. We report the results of an experiment in which subjects vote on a procedure to allocate a reward to half of them. The first possibility is an explicitly random device: the result of a lottery. The second is either an unpredictable procedure they could interpret as meritocratic, or one that is obviously arbitrary. We run all treatments with and without control. We identify an aversion to lotteries and clearly arbitrary procedures across treatments, even though, on aggregate, subjects do not believe any procedure to give them a higher probability of success and there is no correlation between beliefs and outcomes. In line with the literature, we also find evidence of a control premium in most procedures.