Title: Measuring Integrated Information: Comparison of Candidate Measures in Theory and Simulation,
Abstract: 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 (`$\Phi$') 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. Further, only a subset of the measures appear to
genuinely 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 that may have more general applicability.