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Errorless Irrationality: A unified computational account of the inverse base-rate effect across predictive, observational, and unsupervised procedures

This paper demonstrates that the inverse base-rate effect persists across predictive, observational, and unsupervised learning procedures, leading the authors to propose OSCAR, a new unified computational model that explains this irrational bias through self-generated feedback and successfully accounts for individual differences and eye-tracking data where previous theories failed.

Original authors: Lenard Dome, Andy J. Wills

Published 2026-08-07

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Lenard Dome, Andy J. Wills

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Mystery of the "Wrong" Guess

Imagine you are a detective trying to solve a case, but the clues are tricky. You have a suspect who usually commits crimes on Tuesdays (a common event) and another who only strikes on rare, specific holidays (a rare event). Now, imagine you find a clue that could belong to either suspect. Most people, when faced with this ambiguity, would logically guess the common suspect because they are statistically more likely to be involved. But here's the weird part: human brains often do the opposite. When faced with a confusing mix of clues, we have a stubborn, irrational habit of betting on the rare event. This strange phenomenon is called the Inverse Base-Rate Effect (IBRE). It's a quirk in how we learn and make decisions that has puzzled scientists for decades.

For a long time, the leading theory was that this mistake happens because of "prediction errors." Think of it like a video game where you get a "Game Over" screen when you guess wrong. The theory suggested that our brains learn by trying to avoid these "Game Over" screens. When we guess the common suspect and get it wrong, our brain gets a shock, pays extra attention to the rare clues, and overcorrects, leading us to pick the rare suspect next time. But what if there is no "Game Over" screen? What if we are just watching a movie, or looking at a puzzle with no right or wrong answer? Does our brain still make the same irrational mistake? This question sits at the heart of a new study that dives deep into the mechanics of human learning, asking if our "irrationality" is actually a glitch in how we process information, or if it's a feature that exists even when we aren't being graded.

The Great "No-Feedback" Experiment

In this paper, researchers Lenard Dome and Andy J. Wills decided to test the limits of this "prediction error" theory. They wanted to see if the Inverse Base-Rate Effect would still happen if they removed the teacher, the grade, and the "wrong answer" buzzer entirely. They ran two clever experiments to strip away the usual learning conditions.

In the first experiment, they set up an observational learning scenario. Imagine you are sitting in a waiting room reading case files about patients. You see a patient with a fever and a rash, and the file says, "This person has Disease Z." Then you see another with a headache and a rash, and the file says, "This person has Disease L." You are just reading; you aren't being asked to guess, and you aren't told if you were right or wrong. The clues (symptoms) and the answers (diseases) appear together, so there's no moment of "guessing and failing." Despite the lack of any feedback or "Game Over" moments, the participants still showed the irrational bias. When they were later asked to guess which disease a patient had based on a mix of symptoms, they still leaned toward the rare disease, just like in the traditional tests.

In the second experiment, they went even further to remove any hint of cause-and-effect. They replaced the medical stories with geometric shapes. Imagine a puzzle where you see a square and a circle, and you are told to memorize that this combination belongs to "Group X." Later, you see just a square and a triangle. There is no story about diseases or symptoms; it's just shapes. There is no "teacher" telling you what the answer is. Even in this completely abstract, unsupervised world where no one is judging your guesses, the participants still made the same "irrational" choice, favoring the rare category when faced with a confusing mix of shapes.

The New Theory: OSCAR

Since the old theory (that we learn from mistakes) couldn't explain why the bias happened without a teacher, the authors proposed a new model called OSCAR. You can think of OSCAR as a digital brain that doesn't just predict the future; it tries to reconstruct the whole picture.

Imagine you are looking at a jigsaw puzzle, but some pieces are missing. Instead of just guessing what the missing piece is, your brain tries to imagine the entire image, including the parts you can't see. OSCAR works the same way. It takes the clues it sees (the features) and tries to "complete the pattern" by guessing what the whole set of clues should look like, including the category label. If the brain's guess of the whole picture doesn't match the actual picture it sees, it creates an internal "error signal." This signal isn't coming from a teacher; it's coming from the brain's own attempt to fill in the blanks.

The authors found that this "pattern completion" model could explain the results perfectly. It showed that the brain doesn't need an external teacher to make the Inverse Base-Rate Effect. Instead, the effect is a natural side effect of how our brains organize information: we pay extra attention to the clues that help us distinguish between the common and the rare, and this attention gets skewed in a way that makes us overestimate the rare events when things get confusing.

What This Means

The study confirms that this "irrational" bias is not just a result of us trying to avoid being wrong in a classroom setting. It is a fundamental part of how our brains process patterns, even when we are just watching or memorizing shapes. The researchers used computer simulations to show that their new model, OSCAR, could reproduce the exact same human behavior across all three types of experiments (the traditional one, the observational one, and the unsupervised one).

Furthermore, the model was able to explain some tricky data from eye-tracking studies. Previous theories couldn't explain why people looked at certain clues for longer during training but looked at them equally during the test. OSCAR, with its ability to shift attention based on the specific combination of clues, successfully recreated these eye-movement patterns.

In short, the paper suggests that our "irrationality" isn't a bug caused by bad teaching; it's a feature of a brain that is constantly trying to complete the picture, even when the picture is incomplete. The bias toward the rare event is an emergent property of a system that is very good at learning patterns, even when no one is grading its homework.

Technical Summary: Errorless Irrationality

Problem Statement
The Inverse Base-Rate Effect (IBRE) is a robust cognitive bias where individuals, when faced with ambiguous combinations of features, overweigh rare events despite base-rate information suggesting a common outcome should be more probable. Traditional dominant theories (e.g., Kruschke, 1996, 2001b) explain this irrationality through error-driven attentional reallocation. These models posit that prediction errors during supervised learning drive attention away from shared features toward uniquely predictive features, creating an asymmetric representation (e.g., $C \to rare$ becomes highly salient). A central assumption of these accounts is that the IBRE requires an explicit teaching signal (feedback) to generate the prediction errors necessary for learning. However, this assumption has not been rigorously tested in the absence of supervised feedback.

Methodology
The authors conducted two experiments to systematically remove the components of the predictive-learning design that supply error signals, followed by the development and evaluation of a new computational model.

Experiment 1 (Observational Learning): The authors implemented a standard IBRE design but removed explicit feedback. Participants observed sentences pairing symptoms (features) with diseases (labels) simultaneously (e.g., "John has fever and rash, which belongs to disease Z"). No responses were required during training, and no error correction was provided.
Experiment 2 (Unsupervised Learning): To further eliminate potential causal inferences (e.g., symptoms causing diseases) that might drive internal prediction errors, the authors used abstract geometric shapes. Participants memorized arrangements of shapes where category labels were recast as features ( $X$ and $Y$ ). No causal framing or explicit labels were presented; the task was purely pattern recognition.
Computational Modeling (OSCAR): The authors proposed a new model, OSCAR (Outcome-Specific Configuration-dependent Attention Representation). Unlike traditional feed-forward networks that predict labels based on inputs, OSCAR is a feed-forward auto-associative network.
- Architecture: It treats features and category labels as sharing a single input/output space. The network's goal is pattern completion: reconstructing the full input vector (including absent features) from partial inputs.
- Mechanism: It employs a matrix of outcome-specific attention weights ( $\eta_{ki}$ ) rather than a global scalar salience. Attention is updated via gradient descent on a reconstruction error signal generated internally by the network's attempt to complete the pattern.
- Eye-Tracking Mapping: The model includes a mechanism to map internal attention matrices to predicted fixation times, utilizing uncertainty measures (Shannon entropy) and consensus among features.

Key Results

Persistence of IBRE: In both Experiment 1 (observational) and Experiment 2 (unsupervised), participants exhibited the IBRE. They showed a reliable preference for the rare category label when presented with the ambiguous combination of unique features ($BC$), despite the absence of any external error signal or causal framing. This demonstrates that the irrational bias is independent of supervised learning procedures.
Model Performance:
- Supervised Data: Evaluated on a large preexisting supervised dataset, OSCAR performed competitively against established models (EXIT, NNRAS, DGCM). It achieved a $g$ -distance (a measure of model adequacy combining accommodation and specificity) comparable to the best-performing models.
- Generalization: OSCAR is the only model capable of reproducing the IBRE across all three procedures (supervised, observational, and unsupervised). Competitor models relying on external teaching signals failed in the unsupervised conditions.
- Individual Differences: OSCAR was the first model to reproduce the specific pattern of individual differences observed in humans across all three procedures.
- Eye-Tracking: OSCAR successfully replicated the complex eye-tracking data reported by Don et al. (2019). Specifically, it reproduced the finding that while feature $C$ is fixated longer than $B$ during training (on $AC$ vs. $AB$ trials), fixation times for $B$ and $C$ become equivalent during the test phase on $BC$ trials. Previous models with point-estimate salience could not account for this shift.

Significance and Claims
The paper claims to provide a unified computational account of the IBRE that does not rely on the assumption of error-driven attentional reallocation via external feedback.

Errorless Irrationality: The authors argue that the IBRE is an "errorless irrationality." It emerges from the architecture's internal dynamics (pattern completion and self-generated error signals) rather than as a residue of optimizing against an external teacher.
Architectural Necessity: The results suggest that the effect is located in the architecture itself. The irrational bias is an emergent property of a system that learns environmental regularities through auto-association, where features and outcomes share a representational space.
Theoretical Shift: The work challenges the necessity of prediction-error-driven learning for the IBRE, proposing instead that outcome-specific, configuration-dependent attention within an auto-associative framework is sufficient to explain the bias across supervised, observational, and unsupervised contexts.
Explanatory Power: By successfully modeling both the behavioral bias and the specific eye-tracking dynamics (including the training-to-test shift in fixation), OSCAR offers a more comprehensive explanation than previous accounts, which could explain one but not the other.

The authors conclude that the IBRE does not require a corrective teaching signal; it requires only an endogenous self-generated signal derived from the network's attempt to complete patterns.

The Mystery of the "Wrong" Guess

The Great "No-Feedback" Experiment

The New Theory: OSCAR

What This Means

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