There is a growing interest in the travel behaviour modelling community in using alternative methods to capture the behavioural mechanisms that drive our transport choices. The traditional method has been Random Utility Maximisation (RUM) and recent interest has focussed on Random Regret Minimisation (RRM), but there are many other possibilities. Decision Field Theory (DFT), a dynamic model popular in mathematical psychology, has recently been put forward as a rival to RUM but has not yet been investigated in detail or compared against other competing models like RRM. This paper considers arguments in favour of using DFT, reviews how it has been used in transport literature so far and provides theoretical improvements to further the mechanisms behind DFT to better represent general decision making. In particular, we demonstrate how the probability of alternatives can be calculated after any number of timesteps in a DFT model. We then look at how to best operationalise DFT using simulated datasets, finding that it can cope with underlying preferences towards alternatives, can include socio-demographic variables and that it performs best when standard score normalisation is applied to the alternative attribute levels. We also present a detailed comparison of DFT and Multinomial Logit (MNL) models using stated preference route choice datasets and find that DFT achieves significantly better fit in estimation as well as forecasting. We also find that our theoretical improvement provides DFT with much greater flexibility and that there are numerous approaches that can be adopted to incorporate heterogeneity within a DFT model. In particular, random parameters vastly improve the model fit.

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.

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