Optimal Metacognitive Decision Strategies in Signal Detection Theory
Bibliographic record
Abstract
Signal detection theory (SDT) has long provided the field of psychology with a simple but powerful model of how observers make decisions under uncertainty. SDT can distinguish sensitivity from response bias and characterize optimal decision strategies. Recent work has extended SDT to quantify metacognitive sensitivity. Here we further advance the application of SDT to the study of metacognition by providing a formal account of normative metacognitive decision strategies – i.e., type 2/confidence criterion setting – for ideal observers.Optimality is always defined relative to a given objective. We use SDT to derive formulae for optimal type 2 criteria under four distinct objectives: maximizing type 2 accuracy, maximizing type 2 reward, calibrating confidence to accuracy, and maximizing the difference between type 2 hit rate and false alarm rate. Where applicable, we consider these optimization contexts alongside their type 1 counterparts (e.g. maximizing type 1 accuracy) to deepen understanding. We examine the different strategies implied by these formulae and further consider how optimal type 2 criterion setting differs when metacognitive sensitivity deviates from SDT expectation. We also provide an online toolbox for implementing these analyses.The theoretical framework provided here can be used to better understand the metacognitive decision strategies of real observers. Possible applications include characterizing observers’ spontaneously chosen metacognitive decision strategies, assessing their ability to fine-tune metacognitive decision strategies to optimize a given outcome when instructed, determining over- or under-confidence relative to an optimal standard, and more. This framework opens new avenues for enriching our understanding of metacognition.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.011 | 0.054 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".