Sample size dependence of Occam's razor in human decision-making

To make sense of a noisy world, living beings constantly face decisions between competing interpretations for ambiguous sensory data. This process parallels statistical model selection, where most frameworks, like the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), are based on a trade-off between a models goodness-of-fit and its complexity. The same tradeoff has been observed in humans. However, a core tenet of normative frameworks is that the trade-off should depend on the sample size (N); as more data becomes available, the goodness-of-fit grows faster than the complexity penalty, weakening the overall bias towards simplicity. It is unknown whether humans also conform to this scaling principle, and if so, whether it arises from an optimal computation or a simpler heuristic. Here, we investigate this question using a preregistered visual task where subjects inferred the number of latent Gaussian sources generating clusters of data-points, and where the number of points (N) presented on each trial is varied systematically. We use three kinds of model to describe their behavior: a model with linear scaling of evidence in N (as in BIC and AIC), a model with no scaling, and a model with sub-linear scaling inspired by known biases in numerosity perception. Our results demonstrate that the normative, linear scaling model provides the worst account of human behavior. Instead, we find strong evidence for a sub-linear scaling of sample size. By inferring the shape of this scaling with Gaussian Processes, we reveal a distinct logarithmic trend for smaller N, and a flattening for higher values, both consistent with numerosity perception biases. This finding suggests that, when selecting for competing explanations for sensory data, humans do not perform a principled computation but rather employ a more efficient heuristic that repurposes lower perceptual mechanisms to dynamically weight evidence against model complexity.