Previous research on Bayesian inference, reporting poor performance by students and experts alike, has often led to the conclusion that the mind lacks the appropriate cognitive algorithm. We argue that this conclusion is unjustified because it does not take into account the information format in which this cognitive algorithm is designed to operate. We demonstrate that a Bayesian algorithm is computationally simpler when the information is represented in a frequency rather than a probability format that has been used in previous research. A frequency format corresponds to the way information is acquired in natural sampling—sequentially and without constraints on which observations will be included in the sample. Based on the assumption that performance will reflect computational complexity, we predict that a frequency format yields more Bayesian solutions than a probability format. We tested this prediction in a study conducted with 48 physicians. Using outcome and process analysis, we categorized their individual solutions as Bayesian or non-Bayesian. When information was presented in the frequency format, 46 % of their inferences were obtained by a Bayesian algorithm, as compared to only 10% when the problems were presented in the probability format. We discuss the impact of our results on teaching statistical reasoning.

Most approaches to modeling rational inference do not take inio account that in the real world, organisms make inferences under limited time and knowledge. In this tradition, the mind is treated as a calculating demon equipped with unlimited time, knowledge, and computational might. We propose a family of satisficing algorithms based on a simple psychological mechanism: one-reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality, for example, they neither look up nor integrate all information. By computer simulation, we held a competition between the satisficing Take The Best algorithm and various more "optimal" decision procedures. The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. Most interesting was the flnding that the best algorithms in the competition, those which used a form of one-reason decision making, exhibited a startling "less-is-more" effect: they performed better with missing knowledge than with complete knowledge. We discuss the less-is-more effect and present evidence of it in human reasoning. This counter-intuitive effect demonstrates that the mind can satisfice and seize upon regularities in the environment to the extent that it can exploit even the absence of knowledge as knowledge.