Ubiquitous Log Odds: A Common Representation of Probability and Frequency Distortion in Perception, Action, and Cognition
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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.
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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.
“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.”
From Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty (2021) · cites this paper as [135]
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- Authors
- Zhang, H., & Maloney, L. T.
- Affiliations
- New York University (US)
- Corresponding author
- Zhang, Hang
- Venue
- Frontiers in Neuroscience
- Publisher
- Frontiers Media SA
- Published
- 2012
- Volume
- 6
- Pages
- 1-1
- ISSN
- 1662-453X (ISSN-L)
- 1662-4548
- PMC
- PMC3261445
- OpenAlex
- W1995181543
- Cited by
- 679
- References
- 4
- Citations by year
- 2026: 11 · 2025: 20 · 2024: 23 · 2023: 16 · 2022: 23 · 2021: 89 · 2020: 66 · 2019: 62 · 2018: 62 · 2017: 66 · 2016: 82 · 2015: 54 · 2014: 57 · 2013: 33 · 2012: 15
- FWCI
- 39.60
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by-nc
- Locations
- Frontiers in Neuroscience (publishedVersion, cc-by-nc)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- National Institutes of Health
- National Eye Institute (R01EY019889)
- Topics
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Keywords
- log odds, probability distortion, frequency distortion, signal detection theory, risk and uncertainty, sample size effects
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