Quantum probability: A new method for modelling travel behaviour

Abstract

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.

Identifying and Quantifying Factors Determining Dynamic Vanpooling Use

“…The literature shows a new class of Quantum utility models (QUM), where the user has an unclear sequence of decisions for his final choice, and it is possible to simulate the decisions in the intermediate levels [15]. QUM has been implemented in many recent travel behavior studies mostly related with route choice modeling [16,17].…”

Using latent class and quantum models to value equity in health care: a tale of 2 stories

“…6 Given the success of using the quantum choice model in cognitive psychology and transportation, 1 possible application is to use it to address health equity. This concept of a quantum choice model was adapted from Hancock et al 6,8 Conceptually, a participant would consider a choice task containing 2 alternatives. Under the quantum probability theory, the participant starts with a belief state.…”

“…It can be complex because decision makers may choose an alternative based not only on more attractive concrete attributes of the alternative but also how they believe the alternative to be an overall morally contentious option. 6,8 Recently, quantum probability theory has been introduced in cognitive psychology. 9 One of the key differences of the quantum theory from the classic theories of probability is that the distributivity law of "and" and "or" propositions-A λ (B v C) = (A λ B) v (A λ C)-does not need to hold.…”

Quantum choice models: A flexible new approach for understanding moral decision-making

“…This impact is in part due to the underlying logic of quantum probability theory which revealed a fundamental lack of distributivity of propositions concerning non-compatible features of an observed system (Birkhoff and Von Neumann, 1936). This key difference between classical and quantum logic reveals that under quantum theory, the law of probability following the distributivity of 'and' and 'or' of propositions -A ∧ (B ∨C) = (A ∧ B) ∨ (A ∧C) -may fail to hold (for a detailed example, see Hancock et al 2020).…”

“…Furthermore, quantum models can be used to accurately capture the 'change of decision context and mental state' when moving between choices made under revealed preference and stated preference settings (Yu and Jayakrishnan, 2018). Additionally, it has been demonstrated that quantum probability theory can be implemented into choice models to accurately understand route choice problems as well as best-worst choice behaviour in the context of alternative routes (Hancock et al, 2020). Thus there appears to be ample scope for further developments of quantum choice models, with our previous development of the notion of a 'quantum rotation' within a choice model providing useful transitions across choice contexts.…”