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

Abstract

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.

Cognitive modelling reveals distinct electrophysiological markers of decision confidence and error monitoring

“…Therefore, a substantial number of recent studies have searched for the folded X-pattern to empirically identify correlates of decision confidence (Braun et al, 2018;Fetsch et al, 2014;Herding et al, 2019;Lak et al, 2017;Sanders et al, 2016;Urai et al, 2017). However, it has been shown mathematically that the folded X-pattern is neither a necessary nor a sufficient condition for Bayesian confidence (Adler & Ma, 2018;Rausch & Zehetleitner, 2019b). The present study showed empirically that a second statistical pattern of confidence exists and can be used to identify correlates of confidence.…”

“…However, the folded X-pattern can be misleading about confidence because Bayesian decision theory is compatible with other statistical patterns, too (Adler & Ma, 2018;Rausch & Zehetleitner, 2019b). In addition, in some tasks, confidence empirically increased with stimulus strength in correct trials and to a lesser degree in incorrect trials (Kiani, Corthell, & Shadlen, 2014;Rausch, Hellmann, & Zehetleitner, 2018;Stolyarova et al, 2019;van den Berg et al, 2016), a pattern we refer to as double increase pattern.…”

“…In addition, in some tasks, confidence empirically increased with stimulus strength in correct trials and to a lesser degree in incorrect trials (Kiani, Corthell, & Shadlen, 2014;Rausch, Hellmann, & Zehetleitner, 2018;Stolyarova et al, 2019;van den Berg et al, 2016), a pattern we refer to as double increase pattern. The double increase pattern can be reproduced by a smaller number of mathematical models, including the weighted evidence and visibility (WEV) model (Rausch et al, 2018), the heuristic detection EEG markers of confidence 7 model (Maniscalco, Peters, & Lau, 2016;Peters et al, 2017), and some Bayesian models (Adler & Ma, 2018;Rausch & Zehetleitner, 2019b). For these reasons, it is not legitimate to assume a specific statistical pattern a priori.…”

Distinct temporal difference error signals in dopamine axons in three regions of the striatum in a decision-making task

“…A given model and task structure makes specific predictions on the shape of three key signatures relating stimulus discriminability, choice and confidence. The predictions can vary depending on task design (Adler and Ma, 2018;Rausch and Zehetleitner, 2019), but the structure of our task follows the original predictions (Hangya et al, 2016). Additionally, in our task, the mice combined the information about reward size with the strength of sensory evidence to select an action (confidence, or uncertainty) ( Figure 1).…”

Perceptual modulation of parietal activity during urgent saccadic choices

“…For these interrelations to qualify as 314 signatures of the computation of confidence, certain statistical conditions must be satisfied. Specifically, the 315 counterintuitive behavior of confidence during error trials (i.e., lower confidence for stronger evidence) is 316 expected only when there is no overlap between stimulus distributions, so the mapping between evidence and 317 correct choice is unambiguous (Adler and Ma, 2018), and the evidence guiding the choices does not contain 318 independent trial-by-trial information about its discriminability (Rausch and Zehetleitner, 2018). Critically, 319…”