Definitions I am using:
Compatibilism = An agent will always and only choose according to their greatest desire.
Libertarian Free Will (LFW) = An agent can (at least sometimes) choose from among a range of options, each compatible with their nature.
If Compatibilism is true, then there is literally (and definitionally) only ONE possible outcome at every decision juncture – the greatest desire. Hence, someone with good enough information and models could accurately or even perfectly predict the person’s choice – it is, in a manner of speaking, a known formula that can be calculated. Like a supercomputer conquering the stock market or weather forecasts – under Chaos Theory these things are only seemingly random, but if we knew every variable we could perfectly calculate the outcome.
So God (or a supercomputer) would just need to know the starting parameters of the universe, and then would perfectly predict the ONE outcome possible for every agent in existence ever, simply by calculating the greatest desire in each circumstance. There is literally (and definitionally) NO variance or chaos. There is also much less complexity as one goes further down the chain of intersecting choices, since they all have only one possible respective outcome at each juncture.
But if LFW is true, then no matter how ‘predictable’ all the influencing factors might seem to be, the agent can choose from among a range of options – there is (at least sometimes) the Principle of Alternative Possibilities, more than one possible real choice for the agent to decide upon. So a supercomputer could have perfect data and models from the start of the universe, but FAIL to predict the exact outcomes – because there is REAL variance and chaos. Desires are influences on, but not the cause of a choice. We don’t always choose according to the greatest desire.
Whereas God perfectly knows the outcomes despite the LFW choices of agents (all interacting and intertwining, mind you, increasing quadratically in complexity!) – because God has better than mere calculative algorithms, God has PERFECT MIDDLE KNOWLEDGE.