Confidence is detection-like in high-dimensional spaces

TL;DR

This paper demonstrates that Bayesian confidence estimates in high-dimensional spaces naturally exhibit detection-like behavior due to normalization effects, influencing both human and artificial confidence judgments.

Contribution

It reveals that detection-like confidence is a rational outcome of high-dimensional hypothesis consideration, linking human and neural network confidence behaviors.

Findings

Bayesian confidence shows heightened sensitivity to decision-congruent evidence in high-dimensional spaces.

Normalization of confidence by many unchosen options induces detection-like confidence criteria.

Dimensionality influences positive evidence biases in convolutional neural networks.

Abstract

Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show that Bayesian confidence estimates also exhibit heightened sensitivity to decision-congruent evidence in higher-dimensional signal detection theoretic spaces, leading to detection-like confidence criteria. This effect is due to a nonlinearity induced by normalisation of confidence by a large number of unchosen alternatives. Our analysis suggests that detection-like confidence is rational when participants consider a greater number of hypotheses than assumed by the experimenter. Further, we show that a similar dimensionality-driven mechanism can give rise to and modulate the strength of the positive evidence biases in convolutional neural networks, linking our signal detection theoretic analysis to confidence behaviour in artificial systems.