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1.4. Indifference between Small Differences in Utility or Attribute Values

Random utility-maximizing models assume that individuals select from a set of competing alternatives the one with the maximum utility. Implicitly or explicitly the assumption typically made is that individuals perceive and respond to differences in utilities, however small they may be. However, when applying some simplifying decision strategy, individuals may not perceive small attribute differences and/or may be insensitive to small (perceived) attribute differences. Only when differences exceed a certain threshold, a utility difference will be noticed and/or a choice will be made; otherwise the individual will be indifferent.

This concept of threshold difference has a long history outside of transportation research. Quandt (1956) argued that an indifference band surrounds the utility derived from a commodity. Small differences in the quantity of a product consumed will not affect an individuals' utility. Similarly, Georgescu-Roegen (1958) suggested that attribute differences between any two commodities are considered only when some 'necessary minimum' is exceeded. In psychology, perception or sensorial thresholds have for long been recognized as a central characteristic of human response to stimuli. For example, Thurstone (1927) argued human's inability to discriminate between very small differences between stimuli.

More recently, Krishnan (1977) formalized thresholds as 'minimum perceivable differences' between the utilities of the alternatives compared. According to his formalization, an individual prefers one alternative to another if its utility exceeds the utility of the other alternative by at least a positive constant Δ, the minimum perceivable difference. Assuming continuous functions over the possible values of the attributes, if the utility difference is less than this threshold level, the individual is assumed to be indifferent. Krishnan incorporated the threshold parameter into a binary logit model and tested the derived model using data on transport mode choice. Results appeared to support the existence of a positive threshold.

This model acknowledges the possible existence of a band of indifference in discriminating utility differences. Individuals only maximize their utility outside this indifference band. However, the postulate leads to intransitivity of indifference when generalized to multiple alternatives. Lioukas (1984) extended Krishnan's model to the multinomial case. His so-called δ-logit model can be expressed as follows:


where δ>0 is a parameter to be estimated.

Cantillo, Heydecker, and de Dios Ortiizar (2006) formulated a similar threshold model, albeit in a dynamic context. Their model assumed that individuals would only perceive differences in utility to the extent that attribute differences over time are larger than attribute-specific thresholds. Variation in thresholds was treated as a function of socio-demographic variables. Otherwise, their model was not fundamentally different from many earlier formulations.

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