Can we get a measure of “complexity” in some sense that make intuitive sense to us (e.g. that human beings are more complex than an onion, and, I dunno, market capitalism is more complex than socialism or some such.)
This is a non-trivial project for a variety of reasons, but fundamentally because it’s a hopelessly vague concept that we have no particular reason to suppose is universal or useful. In my opinion. It certainly looks like one of those things, like say, “a just society”, where in any conversation you have, you and the other person can agree you want it, but only the shallowest of discussions could fail to reveal how much you and that other disagree what it would look like.
I await a proof of my foolishness here, but thus far every time I have seen two eminent figures mention a general measure of complexity in conversation, its role has not been to do what established scientific concepts usually do, which is to provide a useful referent to a quantity whose nature is approximately agreed upon and moreover proven by many trials to be a handy way of capturing some regularity that obtains in the world. Instead it’s a signal that they should both stop doing whatever productive research they were hitherto engaged in in favour of arguing about what “complexity” means, before eventually leaving for a belated and truncated lunch in disgust. (Myself, I instead waste the same amount of time by arguing about whether having the argument is productive or not.)
But that diatribe was fuelled by too much time duelling with my supervisor. On specific problem domains, as opposed to generally, there are some interesting indicators that do what you want over toy domains. See, for example, The Bumper Book of Informations.