This article focuses on anchoring effects in the process of peer reviewing research proposals. Anchoring effects are commonly seen as the result of flaws in human judgment, as cognitive biases that stem from specific heuristics that guide people when they involve their intuition in solving a problem. Here, the cognitive biases will be analyzed from a sociological point of view, as interactional and aggregated phenomena. The article is based on direct observations of ten panel groups evaluating research proposals in the natural and engineering sciences for the Swedish Research Council. The analysis suggests that collective anchoring effects emerge as a result of the combination of the evaluation techniques that are being used (grading scales and average ranking) and the efforts of the evaluators to reach consensus in the face of disagreements and uncertainty in the group. What many commentators and evaluators have interpreted as an element of chance in the peer review process may also be understood as partly a result of the dynamic aspects of collective anchoring effects.