> asked to push a button any time they feel the urge.
Still completely inconsequential choice. Nothing is going to change in lives of these people based on this choice. This is not a "free will"-type of choice people usually think about.
I think this all started with Sam Harris using this argument in his crusade against free will, and some people just picked it up without giving it a second thought.
The argument is that if the choice is unconsequential (like thinking of a random city or pushing one of equally meaningless buttons), Sam sees that as somehow being the "most free of a choice you could think of". But it is the complete opposite to how the real world and real life works!
I would argue that choosing which school to go to, which career to pursue, which food to eat, which person to spend time with - those are real choices, that's where the free will is used. In choices which have consequences. Choices that matter. Choices that require using the consciousness, not appropriating its gargantual power as being a glorified random number generator. Not in a choice that requires no effort, and can be forgotten the moment it is made, because it will have no consequences whatsoever.
Good luck making those real choices being predictable by a computer. When a computer can predict what career I am going to choose or who am going to hire (given real viable choices) - then we can come back and talk about free will. Of course at that point, by definition, we have Strong AI which can predict almost anything and the world will be completely different, beyond our wildest imaginations because we can't see it behind the veil of technological singularity.
These experiments say nothing about free will. (Of course the papers themselves don't pretend to either, just the sensationalist journalists weakly versed in popular philosophy.)