Fig. 8: Model schematic.
From: Prior information differentially affects discrimination decisions and subjective confidence reports
a Model of conditions. In the model, lead decisions occurred under a flat prior. The lead stimulus generated an internal response with added internal noise, forming the likelihood and then posterior distribution. The area (A in Stronger-Lead condition, B in Stronger-Target condition) of the posterior on the chosen side of the decision boundary (vertical dashed line) equals confidence in the lead decision (conflead). conflead formed the strength of the prior for a rightward target stimulus. The target stimulus generated an internal response, forming the target likelihood, which integrated with the prior to give the target posterior (orange). This posterior led to the target decision and confidence rating. The strength of the posterior probability of the winning hypothesis (opaque orange area) is based on the combination of the prior strength (either A or B, depending on condition) and likelihood strength (either B or A, depending on condition). Because these combine to the same posterior strength (A*B or B*A), the model predicted equal accuracy and mean confidence between conditions, given optimal relative weighting of priors and likelihoods. The weighting parameters, wchoice and wconf, scaled the estimated variance of the lead, effectively scaling conflead, and captured the strength of prior that best explains target decisions and confidence ratings, respectively. b Metacognitive noise in the model. In the dual-decision paradigm, the target prior is susceptible to metacognitive noise, since it is based on an internal confidence computation. Metacognitive noise adds noise to the first-order internal response r (from the Type 1 distribution) for the confidence computation. Since r is the mean of the Type 2 distribution on which confidence is computed, this jitters the resulting confidence value (or the yellow area under the distribution—area A in the leftmost panel of this figure). Note that this does not bias confidence, but makes it more variable across trials, and less reflective of accuracy. Since the rightward target decision prior equates to the confidence value on each trial, metacognitive noise also makes the strength of the rightward target decision prior more variable across trials, not biased overall.
