Scientific peer review has been a cornerstone of the scientific method since the 1600s. Debate continues regarding the merits of single-blind review, in which anonymous reviewers know the authors of a paper and their affiliations, compared with double-blind review, in which this information is hidden. We present an experimental study of this question. In computer science, research often appears first or exclusively in peer-reviewed conferences rather than journals. Our study considers full-length submissions to the highly selective 2017 Web Search and Data Mining conference (15.6% acceptance rate). Each submission is simultaneously scored by two single-blind and two double-blind reviewers. Our analysis shows that single-blind reviewing confers a significant advantage to papers with famous authors and authors from high-prestige institutions.