Peer review supports scientific conferences in selecting high-quality papers for publication. Referees are expected to evaluate submissions equitably according to objective criteria (e.g., originality of the contribution, soundness of the theory, validity of the experiments). We argue that the submission date of papers is a subjective factor playing a role in the way they are evaluated. Indeed, program committee (PC) chairs and referees process submission lists that are usually sorted by paperIDs. This order conveys chronological information, as papers are numbered sequentially upon reception. We show that order effects lead to unconscious favoring of early-submitted papers to the detriment of later-submitted papers. Our point is supported by a study of 42 peer-reviewed conferences in Computer Science showing a decrease in the number of bids placed on submissions with higher paperIDs. It is advised to counterbalance order effects during the bidding phase of peer review by promoting the submissions with fewer bids to potential referees. This manipulation intends to better share bids out among submissions in order to attract qualified referees for all submissions. This would secure reviews from confident referees, who are keen on voicing sharp opinions and recommendations (acceptance or rejection) about submissions. This work contributes to the integrity of peer review, which is mandatory to maintain public trust in science.