To answer this question we need something like a formal definition of "free will". The position on LW is generally that no such thing can exist, that the concept is confused and that the question "do we have free will?" dissolves into "why do we sometimes think we have something called free will?"

But I think it might be possible to come up with an actual definition, one where "we don't have free will" makes some kind of a testable prediction.

First I'm going to assert that determinism isn't free will, and randomness isn't free will either. The problem is that with a single individual it's hard to imagine any behavior that couldn't be explained as "determined" or "random". So, nothing testable so far.

But what if we have a group of individuals? What about if they suddenly all change their behavior so that they all gather together in the same public place wearing something purple? This won't happen if the behavior is random - it's impossible (or at least extremely likely) for all those people to randomly switch to the same new behavior pattern. What if the behavior is determined? Then we'd expect there to be some identifiable cause - an organized flashmob or something. But if free will exists, it should at least in principle be possible that everyone just happened to decide to do the same thing at the same time.

I haven't even thought this through enough to make it into a LW discussion post, and there are at least two flaws:

• We need a definition of "identifiable cause". Yudkowsky has provided a definition of causality but it's not one that I intuitively grasp yet so I'm not sure if it can be used here
• The free willers can just change their definition so that people's behavior can be divided into a causal component and a random/uncorrelated component and still there's room for free will there somewhere
• Also I haven't even Googled to see if someone's come up with something like this before and/or refuted it