Distortions of probability information in human judgment: ubiquitous log odds
In “classical” decision under risk, decision makers choose between lotteries. They typically overweight small probabilities and underweight large. I’ll first briefly describe recent experiments (Wu et al., 2009, 2011; Tee et al, 2011; Zhang et al, 2011; Warren et al., 2011) in which we examine human failure in visual and motor tasks that require judgment or manipulation of probability information. Similar patterns of distortion are found in visual frequency estimation, frequency estimation based on memory, and in the use of probability in decision making under risk. I’ll show that probability distortions in all cases (so far) can be approximated by a linear transformation of the log-odds of probability or relative frequency (Zhang & Maloney, 2011). The slope and intercept of the linear transformation control probability distortion. Researchers have not been able to predict or explain the values of slope and intercept observed in experiments across tasks or across participants. In Zhang & Maloney (2011), we focused on one method for presenting probability, the relative frequency of items of one kind in a visual array of items. We developed a model of human distortion of relative frequency and demonstrated in two experiments that we can separately control slope and intercept with high accuracy. Our results support the conjecture that probability is systematically “adapted” to particular tasks much as perceptual information concerning lightness or loudness is transformed. Wild speculation follows. Supported by Grant EY019889 from the National Institutes of Health and the Humboldt Foundation. References Glaser, C. Trommershäuser, J., Mamassian, P. & Maloney, L. T. (2011), Comparison of distortion of probability information in decision under risk and in an equivalent visual task. Psychological Science, in press, 9/8/2011. Tee, J., Zhang, H. & Maloney, L. T. (2011), Judging the probability of the conjunction of independent events: P(A and B) > P(A)P(B). In preparation. Warren, P. A., Graf, E. W., Champion, R. & Maloney, L. T. (2011), Extrapolation under risk: human observers estimate and compensate for exogeneous uncertainty, under review. Zhang, H., Daw, N. & Maloney, L. T. (2011), Testing whether humans have an accurate model of their own motor uncertainty in a speeded reaching task. in preparation. Zhang, H. & Maloney, L.T. (2011), Ubiquitous log odds: the neural representation of uncertainty. In preparation. Short Biography November 29, 2011 Laurence T. Maloney is currently Professor in Psychology and Neural Science at New York University. He has been at New York University since 1988 and was previously Assistant Professor at the University of Michigan, Ann Arbor in Psychology and in Electrical Engineering & Computer Science from 1985 until 1988. He received his PhD in Psychology from Stanford University in 1985, an MS in Mathematical Statistics, also from Stanford, in 1982, and a BA in Mathematics from Yale University, in 1973. In 2008, he received the Humboldt Research Award from the Humboldt Foundation in Germany for his research. In 1987, he shared the Troland Award of the National Academy of Sciences, one of the highest honors possible for a psychologist in the United States. In 1994, he was awarded a one-year Research Fellowship at the Center for Interdisciplinary Studies at Bielefeld University by the German Research Council. He was resident at the Center during 1995-6 as part of a group considering perception and evolution. In 1998, he was named Forchheimer Visiting Professor at Hebrew University, Jerusalem and in 2009 WICN Scholar at Bangor University, Wales. . He has been a visiting professor at several other universities including Freiburg, Giessen, Paris, and Padova. He has published over 130 chapters, proceedings and articles in scientific journals. His research concerns applications of mathematical models to understanding human behavior. His work in the physics and mathematics of color vision resulted in two highly-cited articles in the Journal of the Optical Society of America. His early work in visual cue combination led to a highly-cited review article in Vision Research. His recent work on movement planning and decision making under risk has built a bridge between two previously unrelated fields. This work is an important contribution to the newly emerging field of neuroeconomics. Currently, he and his colleagues are studying color perception and surface material perception in complex, three-dimensional scenes, human performance in movement tasks equivalent to economic games, and face perception.