Stochastic choice with bounded processing capacity

Abstract

We propose and characterize a class of stochastic decision functions for a decision-maker who has a capacity for processing at most $k$-alternatives at a time. When faced with a menu containing more than $k$ alternatives, she randomly chooses a sub-menu of size $k$ with uniform probability and selects the best alternative according to a strict ordering $\succ$. For smaller menus, she chooses the best alternative according to $\succ$.