Abstract
Metacognition, the ability to assess the quality of our own decisions, is a critical form of higher-order information processing. Metacognitive efficiency is therefore an essential measure of cognitive capability. When making decisions is simple, metacognitive judgments are also straightforward; thus, assessing metacognitive efficiency requires normalizing for the quality of underlying task performance. This is duly common in measures of efficiency popular in perceptual decision-making such as the M-ratio. However, such normalization is hard in reinforcement learning problems, because task difficulty changes dynamically. We therefore repurposed the central idea underlying the M-ratio, using confidence judgments to fashion a notional decision-maker (which we call a Backward model), assessing metacognitive sensitivity according to the quality of its virtual decisions, and quantifying metacognitive efficiency by comparing virtual and modelled actual qualities in the original decision-making task. We used simulated and empirical data to show that our measure of metacognitive sensitivity, the Backward performance, has comparable properties to other measures such as quadratic scoring, and that our measure of efficiency, the MetaRL.Ratio, is independent of empirical performance and is preserved across levels of task difficulty. We suggest that the MetaRL.Ratio as a promising tool for assessing metacognitive efficiency in value-based learning/decision-making.