Peer review often involves reviewers submitting their independent reviews, followed by a discussion among reviewers of each paper. A question among policymakers is whether the reviewers of a paper should be anonymous to each other during the discussion. We shed light on this by conducting a randomized controlled trial at the UAI 2022 conference. We randomly split the reviewers and papers into two conditions--one with anonymous discussions and the other with non-anonymous discussions, and conduct an anonymous survey of all reviewers, to address the following questions: 1. Do reviewers discuss more in one of the conditions? Marginally more in anonymous (n = 2281, p = 0.051). 2. Does seniority have more influence on final decisions when non-anonymous? Yes, the decisions are closer to senior reviewers' scores in the non-anonymous condition than in anonymous (n = 484, p = 0.04). 3. Are reviewers more polite in one of the conditions? No significant difference in politeness of reviewers' text-based responses (n = 1125, p = 0.72). 4. Do reviewers' self-reported experiences differ across the two conditions? No significant difference for each of the five questions asked (n = 132 and p > 0.3). 5. Do reviewers prefer one condition over the other? Yes, there is a weak preference for anonymous discussions (n = 159 and Cohen's d= 0.25). 6. What do reviewers consider important to make policy on anonymity among reviewers? Reviewers' feeling of safety in expressing their opinions was rated most important, while polite communication among reviewers was rated least important (n = 159). 7. Have reviewers experienced dishonest behavior due to non-anonymity in discussions? Yes, roughly 7% of respondents answered affirmatively (n = 167). Overall, this experiment reveals evidence supporting an anonymous discussion setup in the peer-review process, in terms of the evaluation criteria considered.

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