The logic is odd but strait forward. Basically, free will requires people to make choices independent of the past state of the universe. Aka if you replayed to universe up to this point several times they would not always respond in the same way.
If that's the case people should be able to make unpredictable choices by definition. However, when asked to be unpredictable they fail. So, at best people have a limited form of free will.
PS: This is something of an upper bound. At the other end, if replaying someone's life they only have a single non predictable choice they they may have free will. Similarly if they make the same choices in a very large number of universes and only make a different choice in one you could still argue that that's free will. But, the lower bound is not that meaningful of a distinction.
Well OK, but if you want nondeterministic behavior, you can find a source of entropy and make decisions based on a random number (e.g. flip a coin). You chose to do it and it invalidates the hypothesis, because if you replay the universe up to this point, you won't behave in the same way and the choices you just made by flipping a coin are independent of the past state of the universe.
So what am I missing, as I feel we are going into non-falsifiable territory.
If you decide to follow an entropy source and I see the same output as you I can predict your behavior. Free will must be unpredictable as it does not depend on the past state of the universe. (Unless you mean an entropy source outside of the 'universe' which is a rather strange a circular requirement for free will.)
Now, you can argue for a lesser form of free will which is influenced, but not dependent on the state of the universe. However, that's progress even if somewhat obvious.
I've always found that these "Quick, don't think of 'x'" things are a silly example. You end up thinking of X the moment you read X, just before it gets put in context of "not" and "think". It's like telling the parser not to tokenize a given word. Then there's automaticity, which you have to turn off, which is made harder by "Quick", further setting you up to think further of elephants till you get around to grasping the meaning of the phrase.
If that's the case people should be able to make unpredictable choices by definition. However, when asked to be unpredictable they fail. So, at best people have a limited form of free will.
PS: This is something of an upper bound. At the other end, if replaying someone's life they only have a single non predictable choice they they may have free will. Similarly if they make the same choices in a very large number of universes and only make a different choice in one you could still argue that that's free will. But, the lower bound is not that meaningful of a distinction.