Converging Information-Theoretic Measures of Metacognitive Efficiency

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 such quantities as meta − d′ − d′ , or M− ratio [1,2]. 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 relay on unwarranted parametric assumptions, and they fall short of accommodating the granularity of confidence ratings. Two recent papers by Dayan [3] and Fitousi [4] have proposed information-theoretic measures of metacognitive efficiency that can ameliorate these problems. Dayan suggested meta − I, and Fitousi proposed: meta − U, meta − KL, and meta − J . 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 convergence of these measures in a concrete behavioral task using two independent data sets. The present results supported the viability of these novel indexes of metacognitive efficiency, and provide substantial empirical evidence for their convergence.