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Chapter 3 Relative Utility Modelling

Junyi Zhang


Purpose – The chapter outlines the principles underlying relative utility models, discusses the results of empirical applications and critically assesses the usefulness of this specification against commonly used random utility models and other context dependence models. It also discusses how relative utility can be viewed as a generalisation of context dependency.

Theory – In contrast to the conventional concept of random utility, relative utility assumes that decision-makers derive utility from their choices relative to some threshold(s) or reference points. Relative utility models thus systematically specify the utility against such thresholds or reference points.

Findings – Examples in the chapter show that relative utility model perform well in comparison to conventional utility-maximising models in some circumstances.

Originality and value – Examples of relative utility models are rare in transportation research. The chapter shows that several recent models can be viewed as special cases of relative utility models.

Keywords: Relative utility; multiple context dependency; prospect; regret minimisation; advantage maximisation

3.1. Introduction

In the early 2000s, the author with his colleagues introduced in the travel behaviour research community a discrete choice model based on the concept of relative utility (Zhang, Timmermans, Borgers, & Wang, 2004). Several considerations motivated this new model development. First, the validity of discrete choice models, such as the multinomial logit model, that exhibit the independence of irrelevant alternatives (IIA) property was questionable. With few exceptions (e.g. Borgers & Timmermans, 1987) the travel behaviour research community tried to relax this property by allowing for variance differences and covariances in the error term structures of the utility function. It seemed that there was a 'culture' in the choice modelling community that advanced choice models must include complicated error term structures. In other words, complicated error term structures had become synonymous with advanced choice models. However, we felt it is next to impossible to judge whether assumptions about error terms are correct or not. More importantly, from the perspective of supporting policy decisions, it is reasonable to argue that modelling innovation should focus on observed factors rather than on unobserved factors.

Second, although it has been long argued that utility is a relative concept, the ways this notion is reflected in the modelling process were questionable. Looking at modelling practice, conventional utility-based choice models mainly assume that at least one of constant terms in the utility functions is zero. With this assumption, utilities of other alternatives in choice set can be quantitatively measured. In theory, any constant term can be treated as a reference and changing this reference, in case of the most popular linear utility function, does not affect choice behaviour. However, as argued by Kahneman and Tversky (1979), Tversky and Kahneman (1992) and Tversky and Simonson (1993), choice behaviour depends on status quo or reference point(s) and a change of reference point might lead to preference reversal. In this contention, models need to accommodate the existence of various reference points. Third, decision-makers may not treat all alternatives in a choice set equally. Possible reasons include lack of information, tendency of simplifying complex decision-making tasks due to limited information processing capabilities, personal liking or taste, etc.

Thus, the guiding argument was that choice behaviour is context dependent. The importance of incorporating context dependency into choice models has been recognised for about half a century. Earlier studies, dealing with spatial choice behaviour (e.g. Rushton, 1969), argued that individual preference does not exist independently of the environment where the decision is made. Since then, various researchers confirmed the existence of context dependency with respect to various types of human decisions, such as Lichtenstein and Slovic (1971), Borgers and Timmermans (1988), Oppewal and Timmermans (1991), Tversky and Kahneman (1992), Tversky and Simonson (1993), Kokinov and Petrov (2001) and McFadden (2001). In particular, existing studies have repeatedly shown that context-dependent preferences are not mere artifacts but robust features of actual behaviour (e.g. Swait et al., 2002). Thus, the formulation of context-dependent models was felt necessary and it has remained an active field of development ever since.

A unified and widely acknowledged definition of context, however, does not exist. The concept has been described inconsistently in different disciplines and even in different studies in the same discipline. Zhang et al. (2004) attempted to provide a unified definition by identifying three types of context: alternative- specific, individual-specific and circumstantial contexts. Furthermore, they proposed adopting the concept of relative utility to represent context dependency in a systematic way. They argued that an individual evaluates an alternative in a choice set by comparing it with other alternatives (alternative-oriented relative utility]), perhaps with the alternatives the individual chose in the past (time-oriented relative utility), and/or with the alternatives chosen by other individuals (decisionmaker-oriented relative utility). Relative utility argues that utility is only meaningful relative to reference point(s), which is consistent with prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). By contrast, relative utility allows the inclusion of multiple reference points in a systematic way. The influence of multiple reference points reflects general features of human decisions (e.g. Lin, Huang, & Zeelenberg, 2006; Koop & Johnson, 2012). When people make choices, they may have limited information and/or may not have enough time (i.e. bounded rationality may exist). In such situations, setting some reference point(s) may be useful to simplify the decision. Single reference point may be acceptable, but multiple reference points are probably much better because they may lead to a higher degree of satisfaction with the decision.

In the remaining part of this chapter, first relative utility modelling efforts under the principle of relative utility maximisation will be discussed. Next, results of empirical studies will be summarised to assess the usefulness of relative utility models against commonly used random utility models and clarify how relative utility can be viewed as a generalisation of context dependency models. Finally, major findings from both empirical and conceptual perspectives will be summarised and future research issues will be discussed.

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