Peer review is the backbone of academia and humans constitute a cornerstone of this process, being responsible for reviewing papers and making the final acceptance/rejection decisions. Given that human decision making is known to be susceptible to various cognitive biases, it is important to understand which (if any) biases are present in the peer-review process and design the pipeline such that the impact of these biases is minimized. In this work, we focus on the dynamics of between-reviewers discussions and investigate the presence of herding behaviour therein. In that, we aim to understand whether reviewers and more senior decision makers get disproportionately influenced by the first argument presented in the discussion when (in case of reviewers) they form an independent opinion about the paper before discussing it with others. Specifically, in conjunction with the review process of ICML 2020 -- a large, top tier machine learning conference -- we design and execute a randomized controlled trial with the goal of testing for the conditional causal effect of the discussion initiator's opinion on the outcome of a paper.