Free will is "compatible" with determinism not because of chaos. Free will requires both determinism and predictability, as one can determine the future according to own preferences exactly because the future is predictable to a sufficient extent (for each possible action). The future is mathematically definite, it never changes, just as past never changes (for that would require the confused meta-time). You determine the future, with your freedom to determine your own actions (for the actions are defined in terms of your thoughts; you are stuff physics). Chaos, making predictability more difficult, is actually a force against free will.
Also, existence of Laplace's demon is perfectly epiphenomenal to what happens within physics, not affecting anything.
It is possible for universes to exist that allow what we'd call free will but don't have determinism or predictability. Quantum mechanical universes, for example (as long as the universe really contains everything).
A practical albeit fictional application of the philosophical conclusion that free will is compatible with determinism came up today in a discussion about a setting element from the role-playing game Exalted
(5:31:44 PM) Nekira Sudacne: So during the pirmodial war, one Yozi got his fetch killed and he reincarnated as Sachervell, He Who Knows The Shape of Things To Come. And he reincarnated asleep. and he has remained asleep. And the other primordials do all in their power to keep him asleep. and he wants to be asleep.
For you see, for as long as he sleeps, he dreams only of the present. should he awaken, he will see the totaltiy of exsistance, all things past and future exsactly as they will happen. quantumly speaking he will lock the universe into a single shape. All things that happen will happen as he sees them happen and there will be no chance for anyone to change it. effectivly nullifying chance for change. Even he cannot alter his vision for his vision takes into account all attempts to alter it.
And there's a big debate over rather or not this is a game ending thing. Essentially, does predestination negate freewill or not
(5:32:17 PM) Nekira Sudacne: and this is important, because one of the requirements for Exaltation to function is freewill. if Sachervell is able to negate freewill, then Exaltations will cease to function
(5:32:44 PM) Nekira Sudacne: and maddenly enough the game authors are also on the thread arguing because THEY don't agree where to go with it either :)
(5:38:02 PM) rw271828: ah, well I happen to know the answer :-)
(5:39:23 PM) rw271828: one of the most important discoveries of 20th-century mathematics is that in general the behavior of a complex system cannot be predicted -- or rather, there is no easier way to predict it than to run it and see what happens. Note in particular:
(5:39:41 PM) rw271828: 1. This is a mathematical fact, so it applies in all possible universes, including Exalted
(5:40:01 PM) rw271828: 2. Humans and other sentient lifeforms are complex systems in the relevant sense
(5:41:33 PM) rw271828: so if you postulate an entity that can actually see the future (as opposed to just extrapolate what is likely to happen unless something intervenes), the only way to do that is for that entity to run a perfect simulation, a complete copy of the universe
(5:42:50 PM) rw271828: if you're willing to postulate that, well fine, continue the game, and just note that you are running it in the copy the entity is using to make the prediction - the people in the setting still have free will, it is their actions that determine the future, and thus the result of the prediction ^.^
(5:43:04 PM) Nekira Sudacne: Hah. nice one