Optimal metacognitive decision strategies in signal detection theory

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. Whereas classical SDT pertains to "type 1" judgments about the world, recent work has extended SDT to quantify sensitivity for metacognitive or "type 2" judgments about one's own type 1 processing, e.g. confidence ratings. 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. 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.