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A normative Bayesian inference model of retrospective confidence. For two exhaustive alternatives with equal prior probabilities, let $L=\log [p(E\mid H_1)/p(E\mid H_0)]$ be the log-likelihood ratio. Bayes' theorem gives posterior odds $e^L$. Choosing the alternative with the larger posterior yields $P(\text{correct}\mid E)=(1+e^{-|L|}{)}^{-1}$. Unequal priors add prior log odds; choosing a different action changes which posterior probability is appropriate. This calculation does not establish that an observer knows the true likelihoods.

The useful distinction in George Armitage Miller's position is between experiencing a mental event and knowing how that event was produced. An answer, image or feeling of difficulty can enter consciousness while the computations producing it remain inaccessible. Experiencing an intermediate thought also does not reveal the neural or cognitive mechanism generating that thought. Thus a restriction on introspection into mechanisms is compatible with awareness of some intermediate stages of reasoning.

There is evidence against treating an explanation of one's behaviour as a transparent record of its causes. Richard E. Nisbett and Timothy D. Wilson distinguished causal accounts constructed from plausible beliefs from direct access to the relevant processing.^[ref] A particularly clear experimental test is choice blindness: participants chose between faces, but the experimenter sometimes presented the rejected face as the selected one. Some participants accepted the substitution and explained the choice they had not made.^[ref] This challenges the reliability of retrospective causal explanations. It does not establish that every report of a current experience is false: noticing a vivid image and explaining why one preferred a face are different reporting tasks.

Metacognition does not require a complete inspection of the processes being monitored. A judgment of learning can use how easily an answer is retrieved; a retrospective confidence judgment can use the strength or consistency of available evidence. Such metacognitive monitoring is useful when these cues predict future recall or present correctness, even if the participant cannot explain why a cue is informative. A useful experimental distinction is consequently between report content, predictive accuracy and causal access. Measuring one does not settle the others.

Second-order inference about decisions provides a computational possibility: the observer estimates the correctness of a decision from partially shared evidence and the action taken, rather than reading an infallible internal label.^[ref] The computation producing this estimate can itself remain unconscious. Calling it second order specifies what it estimates, not a requirement that a person verbally reflect upon it.

The strongest interpretation of Miller's claim would exclude experience of any unfolding thought. That goes further than the evidence just considered. A person can report successive candidate answers, detect uncertainty, or notice attention drifting, while misdescribing the mechanisms responsible. Conversely, asking for an explanation can create a new inferential task, so a fluent explanation after the event is weak evidence that the same reasoning caused the original decision. Immediate reports, independent performance measures, experimentally manipulated cues and interventions on the proposed mechanism provide stronger tests than introspective plausibility alone. A defensible theory allows informative but selective access to mental states, with fallible inference about their causes; it need not choose between complete transparency and complete ignorance.

Metamemory includes several judgments with different targets: a judgment of learning predicts later recall, a feeling of knowing predicts whether currently unrecalled material could be recognized, and retrospective confidence evaluates an answer already produced. Their accuracy can depend on different information. Agreement between two judgments is therefore not sufficient evidence for one directly inspected memory-strength variable.

In Asher Koriat's cue-utilization approach to metamemory, intrinsic metamemory cues concern the material, extrinsic metamemory cues concern study conditions, and mnemonic cues concern the learner's current processing experience. Paired-associate experiments compared item difficulty, repetition and study duration with both learning predictions and later recall. Item difficulty affected both measures, whereas some changes in study conditions improved recall more than judgments anticipated. Practice could improve item discrimination while producing underconfidence.^[ref] The different patterns argue against treating all judgments as an identical readout of eventual memory performance.

A useful manipulation changes an accessible cue while measuring whether memory changes with it. Matthew G. Rhodes and Alan D. Castel varied the printed size of studied words and collected itemwise learning predictions before a free-recall test. Larger words received higher predictions, despite little corresponding recall advantage; the effect changed when more diagnostic associative information was available.^[ref] This is evidence for cue use and cue competition, rather than evidence that large print inevitably improves learning. A cue's influence on a judgment and its validity for predicting memory must be measured separately.

The timing and content of the judgment matter too. Thomas O. Nelson and John Dunlosky found a delayed judgment-of-learning effect; their subsequent manipulation showed a strong benefit for delayed judgments made from the cue alone, with little corresponding benefit when the cue and target were both displayed.^[ref] A cue-alone test permits a retrieval attempt resembling what will be needed later; seeing the answer can instead make it accessible without establishing that it could be independently recovered. Delay alone is therefore an incomplete description of the effect.

These findings have three implications. First, a cue-based judgment can be accurate without privileged access to a stored trace: accuracy depends on the relation between the sampled cues and the eventual test. Second, metacognitive calibration and metacognitive resolution can change separately. Learning predictions can become better at ranking items while being systematically too low overall. Third, monitoring affects metacognitive control. If an easily read item is mistakenly considered learned, a learner may stop studying it too early. An appropriate study therefore measures subsequent choices and recall, rather than assuming that a changed confidence report necessarily improves learning.

Multiple cues do not imply that every cue has an independent additive weight, nor that the same weights hold across tasks. To distinguish models, factorially manipulate candidate cues, control prior knowledge and test format, and predict judgments separately from memory outcomes. Include delayed and immediate judgments without assuming that eliciting a judgment is itself behaviourally inert. The evidence supports context-sensitive inference from several cues, with predictable successes and illusions, rather than one universally accurate memory gauge.

A common computational target is plausible: retrospective confidence evaluates whether an already selected answer is correct. In a Bayesian inference model this can be written $P(\text{selected answer correct}\mid \text{available evidence, action})$. The evidence might be a sensory signal in perception or retrieved information in memory retrieval. A shared target does not require the same evidence representation, parameters or neural implementation in both domains.

A basic signal detection theory account illustrates the common structure. Two alternatives generate different distributions of internal evidence, the decision selects an alternative, and confidence reflects evidence relative to the decision boundary. With equal prior probabilities and two alternatives, let $L$ be the log-likelihood ratio for the observed evidence. For the alternative with the larger posterior probability, confidence as posterior correctness probability givesThis is a normative consequence of the assumed model, rather than a universal empirical law. The same algebra can describe old/new recognition or a perceptual discrimination only when their assumed likelihoods, priors and decision rule justify it. An old/new discrimination also has a different response structure from comparing two simultaneously presented objects.

A different common account is self-consistency theory of confidence: confidence tracks how consistently a choice is supported across sampled representations. Asher Koriat found predictions of this account, previously applied to knowledge judgments, also held in perceptual judgments.^[ref] Its distinctive implication is that confidently repeated errors are possible when misleading evidence consistently favours the wrong choice. Reliable internal agreement need not entail external correctness. This differs from simply identifying subjective confidence with an objectively calibrated posterior.

Important limitations remain. Recognition can be supported by familiarity and recollection, while a perceptual choice may depend on a currently visible stimulus. The content and timing of evidence differ. Confidence can incorporate an additional retrieval attempt, response fluency, or evidence acquired after the initial decision. A common computation can therefore give different levels of metacognitive efficiency across tasks without requiring a wholly different function for confidence. Conversely, similar average rating curves do not prove a single mechanism: quite different latent processes can produce them.

Second-order inference about decisions makes the relation explicit by distinguishing the information supporting the decision from the partially correlated information supporting its evaluation.^[ref] A model in which confidence has exactly the same evidence as the choice is a stronger hypothesis than a model with a shared inferential goal and separate noisy samples. Error detection and later changes of mind are useful tests because they constrain what further information confidence can use.

Strong evidence for a common mechanism would include quantitative predictions across domains, transfer to a new domain after controlled training, and common effects of selective interventions after matching first-order performance. A shared brain region or a cross-task correlation alone is insufficient: task demands and measurement reliability can produce either apparent commonality or apparent dissociation. The most defensible common basis is a family of evidence-based evaluations of correctness, while the claim of one identical process for memory and perception remains substantially stronger.