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3.5. Conclusion

In this chapter, the principle of relative utility maximisation has been discussed. It allows modelling context dependencies and bounded rationality. Focusing on the alternative-oriented contexts, advantages of relative utility over other concepts that represent context dependencies were discussed and empirically confirmed by comparing relative utility models with conventional random utility maximisation models, and two competing context dependency models (i.e. RRM and RAM models). Consistent improvements in model accuracy and significant context dependency parameters using different data sets provide additional evidence that context dependencies are not an exceptional phenomenon, but rather a robust feature of actual human behaviour. Alternative/attribute-based comparisons, non-linear and asymmetric responses, and relative interest are identified as powerful constructs to represent various context dependencies.

Relative utility models can deal with alternative-based and attribute-based context dependences, whereas RRM and RAM models can only treat attribute-based context dependencies. Attribute-based comparisons between alternatives allow analysts to capture the substitution/similarity and choice set composition effects. Both relative utility models and RRM/RAM models allow for the existence of multiple context dependencies. Since relative utility models with prospect (i.e. MPRI model), RRM and RAM models allow for non-linear comparisons, the compromise effect and the dominated-alternative effect can be explicitly represented. The shortcoming of the RRM model (e.g. it ignores the influence of advantageous alternatives) is overcome by the RAM model while the shortcoming of the RAM model (e.g. it pays less attention to the relative disadvantages, an approximate of regret) is overcome by the RRM model. Relative utility models share the advantages of RRM and RAM models and do not suffer from their disadvantages, but relative utility models without prospect implicitly assume that marginal responses to relative advantages (gain) and disadvantages (loss or regret) are symmetric. All the above models do not have the IIA property because other alternatives in the choice set or their attributes are treated as reference points in defining the relative utility of an alternative under study.

The concepts of relative interest and weight have several attractive features. First, it is the unequal relative interest parameters across alternatives and/or weight parameters that make relative utility models non-IIA models without introducing any additional information. Second, these two types of parameters increase the variation level of the utility function and as a result, are helpful in improving model accuracy. Third, heterogeneous responses to alternative attributes at the alternative level can be easily represented by defining them as a function of observed factors. Fourth, it is easier to introduce these concepts in any utility-based choice model. Finally, it is possible to approximately represent endogenous generation of choice set using a one-step modelling approach rather than the conventional problematic two-step approach.

It should be noted that the differences in model accuracy between relative utility models and RRM and RAM models are not large. Therefore, it should be concluded that introducing non-linear context dependency together with relative interest can improve the accuracy of choice models. Relative utility covers all features of the RRM and RAM models in a more comprehensive way. Thus, relative utility is a more general concept and can be viewed as a generalisation of context dependent models.

The present chapter has only considered one type of context dependency. More research should be devoted to decision-maker and time-oriented relative utility. In theory, these two types of relative utility can be also specified using the similar difference-based utility function. To represent how individuals care about and respond to the actions of others, Clark and Oswald (1998) defined the utility function based on an alternative ratio-based comparison in addition to the difference- based comparison. The ratio-based comparison is the same as the idea suggested by Wang and Yang (1996). As for the time-oriented relative utility, time-dependent utility models, intertemporal choice models or other dynamic models might be relevant if the time-related utility is defined relative to the utility in the past or the future. Last but not the least, Schunk and Betsch (2006) argued that there is a relationship between individual differences in preferred decision mode (intuition vs. deliberation) and the curvature of the individual utility function. Deliberate decision-makers tend to make more risk-neutral decisions and their utility shows a more linear form while intuitive people's decisions mirror a feeling of risk and lead to behaviour which is not risk neutral. Such heterogeneity in either observed or unobserved form should be reflected in the future relative utility model development.

Because relative utility includes conventional utility, rational choice models are nothing but special cases of relative utility models. More importantly, because relative utility includes three types of reference points, it may serve as a meta-concept to represent bounded rationality in a more logical way than other relevant concepts. It should be noted that the concept of relative utility involves a series of unusual complexities, making it difficult to be estimated. Innovative estimation methods should be developed. Under the umbrella of the utility modelling framework, several types of bounded rationality models have been proposed (Rasouli & Timmermans, 2014), including relative utility models. Developing these non-standard choice models has challenged the fundamental properties of conventional utility (i.e. axioms of transitivity, completeness, and continuity) and the argument that choice models based on conventional utility should produce intuitive results. To better represent bounded rationality, however, these fundamental properties have for long been a high wall to climb because they are highly 'respected' by those researchers who believe in the existence of standard (conventional) utility in reality and are charmed by the elegance and beauty of choice models derived from these fundamental properties. In the future, we may need to seriously re-consider whether we should insist in using the name 'utility' to represent actual human decisions or not, and if not, we need to invent a new term to replace the 'utility' concept and consequently create new theories.


This research was supported by the Grants-in-Aid for Scientific Research (A) (No. 22246068) of the Japan Society for the Promotion of Science (JSPS), Japan.

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