Ubiquitous Log Odds: A Common Representation of Probability and Frequency Distortion in Perception, Action, and Cognition

By Hang Zhang, Laurence T. Maloney. Frontiers in Neuroscience, 2012

364 citations recorded by the source corpus.

In decision from experience, the source of probability information affects how probability is distorted in the decision task. Understanding how and why probability is distorted is a key issue in understanding the peculiar character of experience-based decision. We consider how probability information is used not just in decision-making but also in a wide variety of cognitive, perceptual, and motor tasks. Very similar patterns of distortion of probability/frequency information have been found in visual frequency estimation, frequency estimation based on memory, signal detection theory, and in the use of probability information in decision-making under risk and uncertainty. We show that distortion of probability in all cases is well captured as linear transformations of the log odds of frequency and/or probability, a model with a slope parameter, and an intercept parameter. We then consider how task and experience influence these two parameters and the resulting distortion of probability. We review how the probability distortions change in systematic ways with task and report three experiments on frequency distortion where the distortions change systematically in the same task. We found that the slope of frequency distortions decreases with the sample size, which is echoed by findings in decision from experience. We review previous models of the representation of uncertainty and find that none can account for the empirical findings.

Subfields: Cognitive Neuroscience, General Decision Sciences, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/5c26339c0e3952b9849758f23929e2d3d486323c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

In General Decision Sciences

In Management Science and Operations Research

Citations in the corpus

Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty (2020, background): “Zhang and Maloney [135] showed that when people are asked to estimate probabilities or frequencies of events based on memory or visual observations, their estimates are distorted in a way that follows a log-odds transformation of the true probabilities.”
Active Inference, Curiosity and Insight (2017, methodology): “We chose abstract rule learning to illustrate how conceptual knowledge could be accumulated through experience (Botvinick & Toussaint, 2012; Zhang & Maloney, 2012; Koechlin, 2015) and how implicit Bayesian belief updating can be accelerated by applying Bayesian principles not to sensory samples but…”
Self-Evaluation of Decision-Making: A General Bayesian Framework for Metacognitive Computation (2017, background): “…that subtly different beliefs about the true underlying parameters are sufficient to produce a range of patterns of systematic over-or underconfidence, typical of the probability distortions observed in the experimental literature (Drugowitsch et al., 2014; Harvey, 1997; Zhang & Maloney, 2012).”
Combining multiple probability predictions using a simple logit model (2014, methodology): “BothWallsten, Budescu, and Erev (1997) and Zhang and Maloney (2012) recognize the presence of this systematic bias.”
Active Inference: A Process Theory (2017, methodology): “This belief updating is formally identical to evidence accumulation described by drift diffusion or race-to-bound models (Solway & Botvinick, 2012; Zhang & Maloney, 2012; de Lafuente et al., 2015; Kira et al., 2015) and nicely recapitulates the emergence of a choice as evaluation of options…”