Quantum probability: a new method for modelling travel behaviour

There has been an increasing effort to improve the behavioural realism of mathematical models of choice, resulting in efforts to move away from random utility maximisation (RUM) models. Some new insights have been generated with, for example, models based on random regret minimisation (RRM, µ-RRM). Notwithstanding work using for example Decision Field Theory (DFT), many of the alternatives to RUM tested on real-world data have however only looked at only modest departures from RUM, and differences in results have consequently been small. In the present study, we address this research gap again by investigating the applicability of models based on quantum theory. These models, which are substantially different from the state-of-the-art choice modelling techniques, emphasise the importance of contextual effects, state dependence, interferences and the impact of choice or question order. As a result, quantum probability models have had some success in better explaining several phenomena in cognitive psychology. In this paper, we consider how best to operationalise quantum probability into a choice model. Additionally, we test the quantum model frameworks on a best/worst route choice dataset and demonstrate that they find useful transformations to capture differences between the attributes important in a most favoured alternative compared to that of the least favoured alternative. Similar transformations can also be used to efficiently capture contextual effects in a dataset where the order of the attributes and alternatives are manipulated. Overall, it appears that models incorporating quantum concepts hold significant promise in improving the state-of-the-art travel choice modelling paradigm through their adaptability and efficient modelling of contextual changes.