Monotone threshold representations

Motivated by the literature on “choice overload,” we study a boundedly rational agent whose choice behavior admits a monotone threshold representation: There is an underlying rational benchmark, corresponding to maximization of a utility function v, from which the agent's choices depart in a menu-dependent manner. The severity of the departure is quantified by a threshold map δ, which is monotone with respect to set inclusion. We derive an axiomatic characterization of the model, extending familiar characterizations of rational choice. We classify monotone threshold representations as a special case of Simon's theory of “satisficing,” but as strictly more general than both Tyson's (2008) “expansive satisficing” model as well as Fishburn, 1975 and Luce's (1956) model of choice behavior generated by a semiorder. We axiomatically characterize the difference, providing novel foundations for these models.