Eliciting the just-noticeable difference

The evidence from psychophysics suggest that people are unable to discriminate between alternatives unless the options are significantly different. Since this assumption implies non-transitive indifferences, it can not be reconciled with utility maximisation. We provide a method of eliciting consumer preference from observable choices when the agent is incapable of discerning between similar bundles. It is well-known that the issue of noticeable differences can be modelled with semiorder maximisation. 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 Afriat's (1967) theorem to semiorders, rather than utility optimisation. Our approach is constructive and allows us to infer the just-noticeable difference that is sufficient for the agent to differentiate between bundles as well as the "true" preferences of the consumer (i.e., as if perfect discrimination were possible). Furthermore, we argue that the former constitutes a natural measure of how well the preference revealed in the data could be approximated by a weak order. We conclude by applying our test to household-level scanner panel data of food expenditures. Revised June 2017.