Neuroscientist Giulio Tononi has proposed that consciousness is integrated information and can be measured by a quantity called 
, which is a measure of the amount of information that involves the entire system as a whole. I have never really found this theory to be entirely compelling. While I think that consciousness probably does require some amount of integrated information, I am skeptical that it is the only relevant measure. See here and here for some of my previous thoughts on the topic. One of the reasons that Tononi has proposed a single measure is because it is a way to sidestep what is known as “the hard problem of consciousness”. Instead of trying to explain how a collection of neurons would be endowed with a sense of self-awareness, he posits that consciousness is a property of information and the more 
one has, the more conscious you become. So in this theory, rocks are not conscious but thermostats are minimally conscious.
Theoretical computer scientist Scott Aaronson has now weighed in on the topic (see here and here). In his inimitable style, Aaronson shows essentially that a large grid of XOR gates could have arbitrarily large
and hence be even more conscious than you or me. He finds this to be highly implausible. Tononi then produced a 14 page response where he essentially doubles down on IIT and claims that indeed a planar array of XOR gates is conscious and we should not be surprised it is so. Aaronson also proposes that we try to solve the “pretty hard problem of consciousness”, which is to come up with a theory or means for deciding when something has consciousness. To me, the fact that we can’t come up with an empirical way to tell whether something is conscious is the best argument for dualism we have. It may even be plausible that the PHPC is undecidable in that solving it would entail the solution of the halting problem. I agree with philosopher David Chalmers (see
here) that there are only two possible consistent theories of consciousness. The first is that it is an emergent property of the brain but it has no “causal influence” on events. In other words, consciousness is an epiphenomenon that just allows “us” to be an audience for the dynamical evolution of the universe. The second is that we live in a dualistic world of mind and matter. It is definitely worth reading the posts and the comments, where Chalmers chimes in.
, which is a measure of the amount of information that involves the entire system as a whole. I have never really found this theory to be entirely compelling. While I think that consciousness probably does require some amount of integrated information, I am skeptical that it is the only relevant measure. See here and here for some of my previous thoughts on the topic. One of the reasons that Tononi has proposed a single measure is because it is a way to sidestep what is known as “the hard problem of consciousness”. Instead of trying to explain how a collection of neurons would be endowed with a sense of self-awareness, he posits that consciousness is a property of information and the more 
one has, the more conscious you become. So in this theory, rocks are not conscious but thermostats are minimally conscious.
