Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon's notion of satisfying, the authors have proposed a family of algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the authors held a competition between the satisfying "Take The Best" algorithm and various "rational" inference procedures (e.g., multiple regression). The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result in an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference.