Signatures of a Statistical Computation in the Human Sense of Confidence

Abstract

Human confidence judgments are thought to originate from metacognitive processes that provide a subjective assessment about one's beliefs. Alternatively, confidence is framed in mathematics as an objective statistical quantity: the probability that a chosen hypothesis is correct. Despite similar terminology, it remains unclear whether the subjective feeling of confidence is related to the objective, statistical computation of confidence. To address this, we collected confidence reports from humans performing perceptual and knowledge-based psychometric decision tasks. We observed two counterintuitive patterns relating confidence to choice and evidence: apparent overconfidence in choices based on uninformative evidence, and decreasing confidence with increasing evidence strength for erroneous choices. We show that these patterns lawfully arise from statistical confidence, and therefore occur even for perfectly calibrated confidence measures. Furthermore, statistical confidence quantitatively accounted for human confidence in our tasks without necessitating heuristic operations. Accordingly, we suggest that the human feeling of confidence originates from a mental computation of statistical confidence.

Figure 1. Statistical decision confidence predicts specific interrelationships between evidence discriminability, choice outcome and confidence

(A) Illustration of the statistical framework for decision confidence. The dashed box delineates variables internal to the decision maker. A presented stimulus d is corrupted in perception, producing percept d̂, which informs the decision, ϑ. Confidence is computed based on the statistical definition. In humans, confidence is then explicitly mapped to a rating scale, producing the measured report. An external evaluation determines decision correctness. B–D: Monte Carlo simulation of the statistical definition of decision confidence. For all panels, evidence discriminability (see Methods) is the absolute distance of the stimulus from zero. (B) Confidence equals accuracy. (C) Average confidence increases with evidence discriminability from 0.75 for correct choices, and decreases for errors. (D) Conditioning psychometric performance on high or low confidence changes its slope.

Figure 2. The human feeling of confidence follows statistical predictions in a perceptual decision task

For all panels, evidence discriminability is the absolute difference to sum ratio of number of left and right clicks in the experienced click train |((L−R)/(L+R))|. (A) Schematic of task events. (B–D) Confidence patterns of a single subject. Thick lines show parameter-free normative statistical model simulations. Thin lines show one-parameter model fits with a confidence efficacy parameter. Each individual subject is shown in Figure S3. (E–G) Combined data of all subjects (n = 5). Error bars show 95% confidence interval of the mean.

Figure 3. The human feeling of confidence follows statistical predictions in on general knowledge decision task

For all panels, evidence discriminability is the log ratio of the national populations compared. (A) Schematic of the general knowledge task. After initiating each trial and following a random delay, subjects were shown the names of two countries and asked to indicate which had a larger population within 3 seconds by pressing a response key. On 90% of trials, subjects then entered their decision confidence. On sensory probe trials (10%), subjects typed the names of the countries they had just compared. Inset panel: general knowledge task psychometric function for 27 pooled subjects (3,450 trials) showing that choice varied as a function of population log ratio. Errors show binomial 95% confidence intervals. (B–D) Confidence patterns of a single subject who completed 1200 trials. Thick lines show the parameter-free model simulation. Thin lines show a single-parameter model fit with a confidence noise parameter (mostly obscured by the thick lines). (E–G) Combined data of 27 subjects, each completing 100–150 trials. Notably, subjects were only 78.6% correct for trials where confidence was 5/5, consistent with 82.3% accuracy on the strongest fifth of the range of presented evidence (panel E). Error bars show 95% confidence interval of the mean.