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

Author summary Confidence in perceptual choices is a degree of belief that a choice about a stimulus is correct. To identify the neural correlates of decision confidence, recent studies have widely used statistical signatures of confidence. The most widely used statistical signature is the folded X-pattern, which entails that the subjective probability of being correct is 0.75 when the stimulus is neutral about the choice, increases with discriminability in correct trials, and decreases with discriminability in incorrect trials. Here, we examine the consequences if key assumptions of the folded X-pattern are violated. If decision makers are provided with evidence about discriminability, objective confidence increases with discriminability for correct and incorrect choices. In addition, if discriminability is varied in discrete levels, confidence in choices about neutral stimuli is not 0.75. Overall, this means that researchers should not search for correlates of confidence by assuming the folded X-pattern as signature of confidence a priori. 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.