Eliciting the just-noticeable difference

The evidence from psychophysics suggest that people are unable to discriminate between alternatives unless the options are sufficiently different. This paper provides a method of eliciting consumer preference from observable choices when the agent can not perfectly discern between bundles that are similar. Since such a behaviour requires for indifferences to be non-transitive, it can not be reconciled with utility maximisation. We approach the issue of noticeable differences by modelling consumer choice with semiorders. Following the tradition of Afriat (1967), we introduce a necessary and sufficient condition under which a finite dataset of consumption bundles and corresponding budget sets can be rationalised with such a relation. The result can be thought of as an extension of the well-known Afriat’s theorem to semiorder, rather than utility maximisation. Our approach is constructive and allows us to infer both the “true” preferences of the consumer (i.e., as if perfect discrimination were possible), as well as the value of the just-noticeable difference that is sufficient for the agent to discern between alternatives. Furthermore, we argue that the latter constitutes a natural, behaviourally founded measure of departures from utility maximisation. We conclude by applying our method to household-level scanner panel data of food expenditures.