We make decisions every day aware that there is usually an element of uncertainty. Given the importance of many decisions, we might expect that human decision makers are very good at compensation for risk, relative frequency, uncertainty, and other forms of probability. Past research demonstrates the opposite: humans make large errors in their perception and use of probability and these errors can have devasting consequences. Moreover, the errors people make are highly patterned. They typically overestimate small probabilities and underestimate large probabilities. Such probability distortions emerge in almost every perceptual or cognitive task that involves probability and are highly similar across different tasks. Apparently the brain is not just ignorant of probability; it works very hard to get it wrong. Why should the brain distort probability?
In an article published in PNAS on August 25th, 2020, titled “The bounded rationality of probability distortion”, Zhang, Ren and Maloney provide an answer to this puzzling question: Probability distortions are consequences of the brain’s dynamic compensations for some intrinsic “bound” on its perceptual and cognitive capabilities. The authors first develop a computational model of the bound and the compensation process and then report an experiment showing that the model accounts for individual human performance in two different cognitive tasks—decision under risk and relative frequency judgments. Last, the authors show that the particular compensation in each experimental condition serves to maximize the mutual information between objective decision variables and their internal representations.
That is, the brain distorts probability to compensate for its own perceptual and cognitive limitations, and by doing so, it sacrifices local accuracy to optimize the overall information transmission over the environment. In this way, probability distortion can be considered as a form of bounded rationality in Herbert Simon’s term.
Hang Zhang is an assistant professor in the School of Psychological and Cognitive Sciences and PI in the McGovern Institute of Brain Research and Peking-Tsinghua Center for Life Sciences at Peking University. Xiangjuan Ren is a postdoctoral fellow in the School of Psychological and Cognitive Sciences at Peking University. Laurence T. Maloney is a professor in the Department of Psychology and Center for Neural Science at New York University.
This research was supported by grants 31871101 and 31571117 from National Natural Science Foundation of China and funding from Peking-Tsinghua Center for Life Sciences.
Article Link: https://doi.org/10.1073/pnas.1922401117