Recent research in group cognition points towards the existence of collective cognitive competencies that transcend individual group members' cognitive competencies. Since rationality is a key cognitive competence for group decision making, and group cognition emerges from the coordination of individual cognition during social interactions, this study tests the extent to which collaborative and consultative decision rules impact the emergence of group rationality. Using a set of decision tasks adapted from the heuristics and biases literature, we evaluate rationality as the extent to which individual choices are aligned with a normative ideal. We further operationalize group rationality as cognitive synergy (the extent to which collective rationality exceeds average or best individual rationality in the group), and we test the effect of collaborative and consultative decision rules in a sample of 176 groups. Our results show that the collaborative decision rule has superior synergic effects as compared to the consultative decision rule. The ninety one groups working in a collaborative fashion made more rational choices (above and beyond the average rationality of their members) than the eighty five groups working in a consultative fashion. Moreover, the groups using a collaborative decision rule were closer to the rationality of their best member than groups using consultative decision rules. Nevertheless, on average groups did not outperformed their best member. Therefore, our results reveal how decision rules prescribing interpersonal interactions impact on the emergence of collective cognitive competencies. They also open potential venues for further research on the emergence of collective rationality in human decision-making groups.