Add to ORKGThis paper experimentally studies an essential institutional feature of matching markets: Randomization of allocation priorities. I compare single and multiple randomization in the student assignment problem with ties. The Gale-Shapley deferred acceptance algorithm is employed after indifferences in school priorities are resolved by either random procedure. The main result is that a significant fraction of individuals prefers multiple to single randomization, although both are equivalent in expectation. Multiple randomization is perceived to be fairer. One theoretical explanation is the failure to disregard compound lotteries. These results show that random procedures are not inherently neutral with respect to preferences and fairness perce...