The demonstration that human decision-making can systematically violate the laws of rationality has had a wide impact on behavioural sciences. In this study, we use a pupillary index to adjudicate between two existing hypotheses about how irrational biases emerge: the hypothesis that biases result from fast, effortless processing and the hypothesis that biases result from more extensive integration. While effortless processing is associated with smaller pupillary responses, more extensive integration is associated with larger pupillary responses. Thus, we tested the relationship between pupil response and choice behaviour on six different foundational decision-making tasks that are classically used to demonstrate irrational biases. Participants demonstrated the expected systematic biases and their pupillary measurements satisfied pre-specified quality checks. Planned analyses returned inconclusive results, but exploratory examination of the data revealed an association between high pupillary responses and biased decisions. The findings provide preliminary support for the hypothesis that biases arise from gradual information integration.