Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task
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...
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2025-03-01
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| description | 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 <i>bias</i>, <i>sensitivity</i>, and <i>efficiency</i>. To do so, they deploy quantities such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi>d</mi><mo>’</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> or the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>−</mo><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">I</mi></mrow></semantics></math></inline-formula> and Fitousi proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">U</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">KL</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">J</mi></mrow></semantics></math></inline-formula>. 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. |
| format | Article |
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| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-03-01 |
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| spelling | doaj-art-4e5da3fc59c24f68aa7dee46ca3ae3822025-08-20T02:17:25ZengMDPI AGEntropy1099-43002025-03-0127435310.3390/e27040353Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching TaskDaniel Fitousi0Department of Psychology, Ariel University, Ariel 40700, IsraelThe 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 <i>bias</i>, <i>sensitivity</i>, and <i>efficiency</i>. To do so, they deploy quantities such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi>d</mi><mo>’</mo></mrow></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> or the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>−</mo><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">I</mi></mrow></semantics></math></inline-formula> and Fitousi proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">U</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">KL</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>e</mi><mi>t</mi><mi>a</mi><mo>−</mo><mi mathvariant="script">J</mi></mrow></semantics></math></inline-formula>. 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.https://www.mdpi.com/1099-4300/27/4/353metacognitionconfidencemetacognitive efficiencymutual informationKL divergenceJeffrey’ divergence |
| spellingShingle | Daniel Fitousi Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task Entropy metacognition confidence metacognitive efficiency mutual information KL divergence Jeffrey’ divergence |
| title | Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task |
| title_full | Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task |
| title_fullStr | Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task |
| title_full_unstemmed | Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task |
| title_short | Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task |
| title_sort | information theoretic measures of metacognitive efficiency empirical validation with the face matching task |
| topic | metacognition confidence metacognitive efficiency mutual information KL divergence Jeffrey’ divergence |
| url | https://www.mdpi.com/1099-4300/27/4/353 |
| work_keys_str_mv | AT danielfitousi informationtheoreticmeasuresofmetacognitiveefficiencyempiricalvalidationwiththefacematchingtask |