Inspired by evidence from cognitive psychology, this article studies a simple choice model in which two systems jointly determine behavior: a fast, effortless, and gullible system 1 and a slow, effortful, and deliberate system 2. By incorporating both sources of "irrational" behavior, our model accounts for many choice anomalies. Nevertheless, we show that the model still possesses empirical content by characterizing it with squeezing conditions directly generalized from standard contraction and expansion conditions. Due to its generality, our model can serve as an umbrella under which three lines of nonstandard choice procedures can be organized: maximization of menu-dependent preference, preference maximization over part of the menu, and the rational shortlisting method. Our model is more than an organizational device because the two systems can be interpreted as "simple and heuristic" and "complex and deliberate" decision-making methods with multiple selves who are divided into coalitions
