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1.1. Framework

Although models of decision-making and choice behaviour differ substantially, they have in common (part of) the following approach. In travel behaviour analysis and related disciplines, the aim of the modelling approach is to predict the choices of different segments of the population, which are assumed to represent observed heterogeneity, related to a particular facet (destination, travel mode, route, departure time, etc.), mostly to support planning processes. Because planning is primarily related to the physical attributes of the transportation and urban system, essentially choice probabilities are predicted as a function of the physical attributes of the spatial setting. Physical attributes may be augmented with other, for example, economic attributes.

Let us first introduce basic notation. The urban-transportation system can be described in terms of a set of i=1, 2, ...,choice alternatives, making up choice set C. Each choice alternative i is characterized by a non-empty set of Ki attributes. To allow that choice sets differ between individuals, let us denote the choice set Cn of individual n. This set of attributes may be identical for the different choice alternatives; for example, a set of generic attributes for shopping centres. It may also (partly) be specific for different alternatives; for example, attributes of transport modes. Let Xik describe the attribute value of alternative i on attribute k. Finally, let the characteristics of decision-makers n = 1, 2, ..., N be described as Ζnj, j = 1, 2, ..., J.

In some modelling approaches, attributes of the choice alternatives are directly linked to choices observed in the real world , . In this case, the researcher has to decide on the set of attributes assumed to influence the choice behaviour of interest. In addition, the choice set C has to be identified. In case of transport mode and departure time choice, this modelling step is trivial. In contrast, identification of the choice set in case of destination and route choice is a challenging and non-trivial task. More detailed approaches involve one or more of the following decision-making steps:

1. Mapping of objective, physical space into a cognitive space, measuring individuals' perception: ;; . This step acknowledges that individuals may have partial (k Î Kni) and imperfect knowledge about the environment surrounding them. Moreover, they may not be familiar with all choice alternatives (). It also contends that individuals base their decisions on their cognitive representations of reality as opposed to reality itself. The notion of imperfect knowledge will be picked up by the mapping function. Any non-linear function or linear function, not running at 45 degrees angle through the origin will describe transformations of objective attribute values into cognitive values. The mapping can be described as ; ; where is any function applied to attribute k. The cognitive representation of choice alternative i of individual n with respect to its attributes can thus be described by vector

I.

2. The transformation of the cognitions into a set of value judgments . The evaluation of attribute values may be based on processing of the absolute values of the attributes only, it may be based on processing of the values of the attributes relative to one or more attribute values of other choice alternatives, or it may be based on processing of the values of attributes relative to some exogenous reference point. This process of integrating the evaluation can be described as ; ; , where is any valuation function applied to attribute k. It may be algebraic (linear or non-linear) or Boolean. This representation allows the valuing function to be individual-specific. Existing models have typically assumed a homogeneous function (in specification and parameters) across all individuals, a function that is homogeneous in specification but not in parameters, or a function that depends on latent classes (specification and/or parameters).

3. The integration of these value judgments into an overall judgment that constitutes the basis for ordering the choice alternatives in order of preference. This process of integrating the evaluation can be described as ;; , where hn is any integration function applied to attribute values Vn&. The integration function defines the functional form of the integration, which represents the assumed underlying decision-making process in mathematical terms, and the weights or importance of the various attributes. It results in an ordered set of overall value judgments (utility, satisfaction, etc.) , on some preference scale. Function h may be algebraic (linear or non-linear) or Boolean.

4. Deciding which choice to make, considering the preferences and the choice set. The ultimate choice process involves a function operating on , which maps the value judgments some final set of choice probabilities,. The choice may depend on the absolute value of ; in other cases, it may depend on a comparison of all choice alternatives in the choice set.

This framework should be instrumental to understanding both rational decisionmaking processes and processes based on bounded rationality. For example, the commonly applied multinomial logit model assumes thatandare linear for all attributes; h is a linear additive function, while q is a logit transformation. Bounded rationality implies that individuals consider only a subset of the potentially influential attributes, and/or in comparing choice alternatives do not differentiate between asymptotically small differences in attribute values, and/or do not consider all alternatives in the choice set, and/or do not seek the optimal choice, based on maximizing their overall judgments.

The models of bounded rationality, discussed in this chapter, have concepts such as utility, attribute importance and thresholds in common. In general, these have been applied in two diverging modelling approaches. Some studies are based on explicit and direct questioning of respondents who are asked to indicate their utility for particular attributes of choice alternatives, threshold and/or attribute importance. Other studies are based on econometric modelling, where one or more of these concepts are treated as parameters that need to be estimated.

The remainder of this chapter discusses a cross-section of existing studies that has addressed these issues. We will first discuss alternatives to classic utility- maximizing behaviour, based on non-compensatory decision rules that do not necessarily lead to optimal choices according to the traditional view. Next, we continue by summarizing attempts of modelling how individuals' decisions may only include a subset of all attributes. Then, we discuss models that assume individuals simplify the decision-making process by ignoring small attribute/alternative differences. Finally, we will consider models that address the problem how individuals reduce a large consideration set into a much smaller consideration set. This is followed by a discussion of some results of empirical applications. Finally, we draw some conclusions.

 
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