Human perception of probabilities - especially very small and very large probabilities - can be markedly distorted and these distortions can lead to potentially disastrous decisions. But why we distort probability has been unclear. Now a team of scientists from New York University and Peking University has published the results of research into the nature of these distortions, which offers potential clues for explaining this phenomenon.
The study team, which included New York University's Laurence Maloney as well as the University of Peking University's Hang Zhang, a professor, and Xiangjuan Ren, a post-doctoral fellow, focussed on developing a model of human cognitive limitations and testing its predictions experimentally.
"Probability distortion limits human performance in many tasks, and we conjectured that the observed changes in probability distortion with task was a kind of partial compensation for human limitations," explains Maloney. "A marathon runner with a sprained ankle will not run as well as she might have with ankle intact, but the awkward, limping gait we observe could in fact be an optimal compensation for injury."
The key step in the model is the recoding of probabilities that depends on the range of probabilities in a task.
"Much like a variable magnification microscope, the brain can represent a wide range of probabilities, but not very accurately, or a narrow range at high precision," explains Maloney. "If, for example, a task involves reasoning about the probability of various causes of death, for example, then the probabilities are all very small (thankfully) and small differences are important. We can set the microscope to give us high resolution over a limited window of very small probabilities. In another task we might accept less precision in return for the ability to represent a much wider range of probabilities."
Zhang, Ren, and Maloney set out to test this model in two experiments, one in which subjects made typical economic decisions under risk (e.g. choosing between a 50:50 chance of $200 and the certainty of $70) and one involving judgements of relative frequency (the relative frequency of black and white dots appearing on a computer screen). The two experiments together tapped into the basic ways we use probability and frequency in everyday life. The researchers found that their model predicted human performance far better than any previous model.
The researchers concluded that the particular compensation in each experimental condition serves to maximize the mutual information between objective decision variables and their internal representations. We distort probability to compensate for our own perceptual and cognitive limitations.
Read the paper, ‘The bounded rationality of probability distortion’ here.