The folded X-pattern is not necessarily a statistical signature of decision confidence

Recent studies have traced the neural correlates of confidence in perceptual choices using statistical signatures of confidence. The most widely used statistical signature is the folded X-pattern, which was derived from a standard model of confidence assuming an objective definition of confidence as the posterior probability of making the correct choice given the evidence. The folded X-pattern entails that confidence as the subjective probability of being correct equals the probability of 0.75 if the stimulus in neutral about the choice options, increases with discriminability of the stimulus in correct trials, and decreases with discriminability in incorrect trials. Here, we show that the standard model of confidence is a special case in which there is no reliable trial-by-trial evidence about discriminability itself. According to a more general model, if there is enough evidence about discriminability, objective confidence is characterised by different pattern: For both correct and incorrect choices, confidence increases with discriminability. In addition, we demonstrate the consequence if discriminability is varied in discrete steps within the standard model: confidence in choices about neutral stimuli is no longer .75. Overall, identifying neural correlates of confidence by presupposing the folded X-pattern as a statistical signature of confidence is not legitimate.