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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 departures from utility maximisation. We conclude by applying our test to household-level scanner panel data of food expenditures.
