Randomness is maximally complex.
I am not sure this is a useful way to look at things. Randomness can be very different. All random variables are random in some way, but calling all of them "maximally complex" isn't going to get you anywhere.
Outside of quantum physics, I don't know what is "a true random output". Let's take a common example: stock prices. Are they truly random? According to which definition of true randomness? Are they random to a superhuman AI?
it's not randomness if it is predictable
Let's take a random variable ~N(0,1), that, normally distributed with the mean of zero and the standard deviation of 1. Is it predictable? Sure. Predictability is not binary, anyway.
we should favor simple explanations over complex explanations
That's just Occam's Razor, isn't it?
Simplicity's advantage is that it minimizes our vulnerability to random noise.
How do you know what is random before trying to model it? Usually simplicity doesn't minimize your vulnerability, it just accepts it. It is quite possible for the explanation to be too simple in which case you treat as noise (as so are vulnerable to it) things which you could have modeled by adding some complexity.
complexity ... is more flexible and sensitive to random changes in input
I don't know about that. This is more a function of your modeling structure and the whole modeling process. To give a trivial example, specifying additional limits and boundary conditions adds complexity to a model, but reduces its flexibility and sensitivity to noise.
general superiority of simple explanations
That's a meaningless expression until you specify how simple. As I mentioned, it's clearly possible for explanations and models to be too simple.
After giving myself some time to think about this, I think you are right and my argument was flawed. On the other hand, I still think there's a sense in which simplicity in explanations is superior to complexity, even though I can't produce any good arguments for that idea.
This essay claims to refute a popularized understanding of Occam's Razor that I myself adhere to. It is confusing me, since I hold this belief at a very deep level that it's difficult for me to examine. Does anyone see any problems in its argument, or does it seem compelling? I specifically feel as though it might be summarizing the relevant Machine Learning research badly, but I'm not very familiar with the field. It also might be failing to give any credit to simplicity as a general heuristic when simplicity succeeds in a specific field, and it's unclear whether such credit would be justified. Finally, my intuition is that situations in nature where there is a steady bias towards growing complexity are more common than the author claims, and that such tendencies are stronger for longer. However, for all of this, I have no clear evidence to back up the ideas in my head, just vague notions that are difficult to examine. I'd appreciate someone else's perspective on this, as mine seems to be distorted.
Essay: http://bruce.edmonds.name/sinti/