The number of boundedly rational choices on four elements.

We use a combinatorial approach to identify and compute the number of non-isomorphic choices on four elements that can be explained by several models of bounded rationality. •These estimates offer a tool to analyze choice experiments designed on four-element sets.•The presented methodology allows the application of an algorithm to estimate the fraction of choices justifiable by these models on finite sets.•Our approach can be extended to evaluate other - existing or future - models of bounded rationality.