Next Article in Journal
Gearbox Composite Fault Diagnosis Method Based on Minimum Entropy Deconvolution and Improved Dual-Tree Complex Wavelet Transform
Next Article in Special Issue
Integrated Information as a Measure of Cognitive Processes in Coupled Genetic Repressilators
Previous Article in Journal
Numerical Study of Double-Layered Microchannel Heat Sinks with Different Cross-Sectional Shapes
Previous Article in Special Issue
What Does ‘Information’ Mean in Integrated Information Theory?
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessArticle
Entropy 2019, 21(1), 17;

Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation

Department of Computing, Imperial College, London SW7 2RH, UK
Sackler Centre for Consciousness Science and Department of Informatics, University of Sussex, Brighton BN1 9RH, UK
Author to whom correspondence should be addressed.
Received: 11 September 2018 / Revised: 13 December 2018 / Accepted: 18 December 2018 / Published: 25 December 2018
(This article belongs to the Special Issue Integrated Information Theory)
PDF [1330 KB, uploaded 28 December 2018]


Integrated Information Theory (IIT) is a prominent theory of consciousness that has at its centre measures that quantify the extent to which a system generates more information than the sum of its parts. While several candidate measures of integrated information (“ Φ ”) now exist, little is known about how they compare, especially in terms of their behaviour on non-trivial network models. In this article, we provide clear and intuitive descriptions of six distinct candidate measures. We then explore the properties of each of these measures in simulation on networks consisting of eight interacting nodes, animated with Gaussian linear autoregressive dynamics. We find a striking diversity in the behaviour of these measures—no two measures show consistent agreement across all analyses. A subset of the measures appears to reflect some form of dynamical complexity, in the sense of simultaneous segregation and integration between system components. Our results help guide the operationalisation of IIT and advance the development of measures of integrated information and dynamical complexity that may have more general applicability. View Full-Text
Keywords: integrated information theory; computational neuroscience; complexity; consciousness integrated information theory; computational neuroscience; complexity; consciousness

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Mediano, P.A.; Seth, A.K.; Barrett, A.B. Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation. Entropy 2019, 21, 17.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top