Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task - Daniel Fitousi (Entropy)
The ability of participants to monitor the correctness of their own decisions by rating their confidence is a form of metacognition. This introspective act is crucial for many aspects of cognition, including perception, memory, learning, emotion regulation, and social interaction. Researchers assess the quality of confidence ratings according to bias, sensitivity, and efficiency. To do so, they deploy quantities such as <semantics>meta−d’</semantics>-<semantics>d′</semantics> or the <semantics>M−ratio</semantics> These measures compute the expected accuracy level of performance in the primary task (Type 1) from the secondary confidence rating task (Type 2). However, these measures have several limitations. For example, they are based on unwarranted parametric assumptions, and they fall short of accommodating the granularity of confidence ratings. Two recent papers by Dayan and by Fitousi have proposed information-theoretic measures of metacognitive efficiency that can address some of these problems. Dayan suggested <semantics>meta−I</semantics> and Fitousi proposed <semantics>meta−U</semantics>, <semantics>meta−KL</semantics>, and <semantics>meta−J</semantics>. These authors demonstrated the convergence of their measures on the notion of metacognitive efficiency using simulations, but did not apply their measures to real empirical data. The present study set to test the construct validity of these measures in a concrete behavioral task—the face-matching task. The results supported the viability of these novel indexes of metacognitive efficiency, and provide substantial empirical evidence for their convergence. The results also adduce considerable evidence that participants in the face-matching task acquire valuable metaknowledge about the correctness of their own decisions in the task.