Economic models of animal behaviour assume that decision-makers are rational, meaning that they assess options according to intrinsic fitness value and not by comparison with available alternatives. This expectation is frequently violated, but the significance of irrational behaviour remains controversial. One possibility is that irrationality arises from cognitive constraints that necessitate short cuts like comparative evaluation. If so, the study of whether and when irrationality occurs can illuminate cognitive mechanisms. We applied this logic in a novel setting: the collective decisions of insect societies. We tested for irrationality in colonies of Temnothorax ants choosing between two nest sites that varied in multiple attributes, such that neither site was clearly superior. In similar situations, individual animals show irrational changes in preference when a third relatively unattractive option is introduced. In contrast, we found no such effect in colonies. We suggest that immunity to irrationality in this case may result from the ants' decentralized decision mechanism. A colony's choice does not depend on site comparison by individuals, but instead self-organizes from the interactions of multiple ants, most of which are aware of only a single site. This strategy may filter out comparative effects, preventing systematic errors that would otherwise arise from the cognitive limitations of individuals.