Random Regret Minimization: An Overview of Model Properties and Empirical Evidence

Abstract

This paper presents an overview of model properties and empirical evidence related to the recently introduced discrete choice paradigm of random regret minimization (RRM). The RRM approach to discrete choice modelling provides an alternative to the conventional, linear-additive random utility maximization (RUM)-based approach which has dominated the field since its inception. Section of Transport and Logistics RRM models postulate that when choosing, decision-makers are concerned with avoiding the situation where one or more non-chosen alternatives perform better than a chosen one in terms of one or more attributes. From this central behavioural premise, semi-compensatory decision-making and choice set composition effects like the compromise effect emerge as RRM model features. Being as parsimonious as RUM's linear-additive multinomial logit model, RRM features logit choice probabilities and is easily estimable using conventional discrete choice software packages. This paper ties together the main insights and results from a number of recent studies that have explored RRM's model properties and empirically tested RRM-based models Delft University of Technology, based on a range of revealed and stated choice data sets. As such, the paper allows for an early assessment of RRM's potential and its limitations as a model of discrete (travel) choice behaviour.

Acknowledgements

Comments by Maarten Kroesen on a draft version of this paper were much appreciated. I am grateful to two unknown referees for making a range of interesting remarks on an earlier version of this paper. Support from the Netherlands Organization for Scientific Research (NWO), in the form of VENI-grant 451-10-001, is gratefully acknowledged.

Notes

Ramos et al. (in press) build on the RRM approach (the 2008 version) to explain repeated route choices with risky travel times, observed in a travel simulator. However, the authors forego the use of error terms and, rather than estimating their RRM model formulation, they perform a grid search to obtain rough proxies for some parameters while keeping the values of other parameters fixed at one. When this particular interpretation of the RRM model is tested against models loosely based on expected utility- and prospect theory-based premises, its performance in terms of predicting route choices is reasonable, though somewhat less than the two competing models.

Related to this: RRM's model estimates are a function of the size of the choice set. Specifically, the additive regret function (which postulates that an alternative's regret is a function of a binary comparison with each of the other alternatives in the set) implies that in the context of larger choice sets, smaller parameter estimates are obtained and vice versa. This is turn implies that when making predictions based on an estimated RRM model, these predictions should refer to a choice set that is of the same size as the one used for model estimation.

Importantly, RRM does not imply non-compensatory behaviour since no attribute value can be a ‘deal-breaker’ and every attribute is considered in the decision-making process. The term ‘semi-compensatory behaviour’ is used to highlight that RRM postulates that even when two attributes are equally important, an improvement in one attribute does not necessarily compensate for an equally large deterioration of the other attribute.

It is important to note at this point that, while in a conventional linear-additive RUM setting VoT can be defined as the ratio of the marginal utility of the time attribute to the marginal utility of the cost attribute, this does not imply that in a RRM setting such an unambiguous link between marginal regret ratios and VoT exists as well. More specifically, the intuition behind RUM's VoT definition follows from its rigorous foundation in welfare economics (e.g. Small and Rosen, 1981). The RRM model lacks such a strong foundation in the axioms of microeconomics, as it has been developed from a more descriptive and behaviour-inspired perspective rather than an axiomatic one. As such, strictly speaking the use of the term VoT in a RRM context is debatable. However, for reasons of clarity of presentation, the VoT terminology will be applied in this paper, for RUM models as well as for RRM models.