A novel behavioral paradigm reveals the nature of confidence computation in perceptual decision making

A central goal of research in perceptual decision-making is understanding the computations underlying choice and confidence. However, revealing these computations requires knowledge of the internal representation upon which the computations operate. Unfortunately, how traditional stimuli (e.g., Gabor patches and random dot kinematograms) are transformed into internal representations of evidence remains unknown, hindering the building of computational models. This study introduces a new behavioral paradigm where subjects discriminate the dominant color in a cloud of differently colored dots. Critically, we show that the internal representation for these stimuli can be described with a simple, one-parameter equation: the representation for n dots follows a Gaussian distribution with a mean of n and SD of alpha*n. In other words, the free parameter alpha controls observer sensitivity, and the SD of internal activations scales linearly with numerosity of dots. We first demonstrate that this one-parameter model explains decision data in complex, 3-choice tasks across two experiments with up to 12 conditions featuring different dot number combinations. Critically, we use this paradigm to test three popular theories of confidence: (1) the Bayesian Confidence Hypothesis (BCH), which assumes that confidence reflects the probability of being correct, (2) the Positive Evidence (PE) model, which assumes that confidence reflects only choice-congruent (i.e., positive) evidence, and (3) the Difference model, which assumes that confidence reflects the evidence difference between the highest and the second-highest signal. We find that the Difference model provides the best fit, followed closely by BCH. In contrast, the PE model provides very poor fits, trailing the Difference model by over 4,000 AIC points in both Experiments 1 and 2. These results establish a new paradigm where a single free parameter can characterize the internal representation across a potentially unlimited number of conditions, enabling the comparison of different theories of perceptual decision making and confidence.