Does even fixed probability imply no free will?

Question

If we have 1000000 identical ppl and we tell them to choose left or right, roughly 50% will choose each direction. Same thing if repeated million times. Then are they really free?

The only definition that makes any kind of sense for free will is that they can work outside the laws of physics.

I think if the % converges to fixed value every time, then they can't be free else that % will be a physical law or due to underlying law.

I'm actually talking about quantum mechanics in this post and was wondering about Dyson's hypothesis of free will for electrons. So, the % in above example is closer to 99.9 than 50.

Edit2: On further analysis I think Dyson is talking about the feeling of free will. I think even he agrees that free will doesn't exist in the sense of what I was talking. He's saying electrons are conscious and have the feeling of free will. This feeling is amplified in human system.

Could Atomic Science Explain Free Will? video with Freeman Dyson.

'The Faith of Scientists: In Their Own Words' edited by Nancy Frankenberry, Freeman Dyson chapter p1923, topic: the argument from design is theological and not scientific.

Answer 1

VERY SHORT ANSWER

Yes, you are correct, libertarian free will is not compatible with a probabilistic "law".

MUCH MORE COMPLICATED ANSWER

You have a lot of suspect assumptions behind your set of questions.

The first is how one gets to reality. The method of science is Locke/Popperian indirect inferential realism. NOT the rationalism implicit in your post (start with rules/assumptions and then derive reality). Indirect realism is tentative, contingent, and in most cases does not support global/absolute claims. Our indirect realism models may, and often do, contradict each other. See quantum dynamics and relativity for an example of this. We think both are "true" but they contradict.

This is a key issue for the reasoning you are using. You are treating logic, deterministic causation, the lawlike nature of science, and physical causal closure as all givens, and dismissing free will based on its being in conflict with them. But multiple incompatible models CAN be "close enough" to true, and be accepted as working hypotheses. And free will is strongly supported by lots of evolutionary evidence (see my answer to this quesiton): Which evolutionary concepts or theories are used to either support or undermine 'perception of free will' as accurate?

Meanwhile our physics is not deterministic (see my answer): Is it the incorrect assumption of an "a priori determined universe", which creates the paradox of determinism versus free will?, it is not "lawlike" https://www.pnas.org/doi/10.1073/pnas.93.25.14256, and there are infinite possible logics not One True Logic https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877. And while your critique of its advocates being unable to identify what is meant by libertarian free will is valid, there is a similar and also valid critique of causation (see my answer here) How is free-will formally defined as distinct from determinism, randomness and determinism-randomness hybrid to support moral responsibility?

So -- your points about logic and definitional problems for libertarian free will are correct, but we still have strong reasons to accept the reality of free will, and instead just acknowledge and live with logical incompatibilities in our worldview, given the MUCH less than ironclad cases for one true logic, physical causal closure, law-like science, etc. None of these current assumptions is likely to be absolutely "true" if we try to project into the future to a fully reconciled worldview.

Answer 2

The observation of consistent statistics of choices in populations of agents do not confirm our disprove common definitions of free will in general.

So if we assume some population of agents having assumedly whatever flavor of free will, a consistent distribution of 50/50 or 40/60 is similar for roughly equivalent choices does not contradict that those agents have free will.

Rational agents can be assumed to make rational choices, so if you ask people to take 100 dollars or swallow poison, it is reasonable to assume most will take the money, and that does not contradict free will as an ability.

More specifically, free will theories do not require every single decision if agents to be made rationally, whether to pick coca cola or Pepsi cola does not need to be a decision made using the capacity of free will.

So even if we did observe consistently bad decision making in population of agents, such as chain smoking or people believing in crazy religious claims, this would still not disprove the ability to make decisions based on free will.

Only if we observed populations of agents consistently incapable of making a given reasonable decision would free will be seriously in doubt. As an example, lack of intelligence restricts certain animals from making available choices that would satisfy best their instinctive needs, which leads to valid inference that in such situations other non-free factors determine the behavior of those animal species.

With humans, such observations have not been consistently found, even if individual humans may e.g. suffer from drug addictions seemingly unable to stop those habits.

Answer 3

I would rather leave this as a comment rather than an answer but I don't have the 50 required rep to do it. You are touching the problem I have with the concept of free will: If someone's behavior isn't determined by the laws of physics alone (for instance because said laws are nondeterministic), then what determines it? Free will comes as a handy rug under which we like to hide the dust under. Is the chance to choose left over right 50%? If so, this is a law. If not then what are the odds? 40%? 20%? 80% "because you're right handed"?

Those are still laws no matter how uneven the distribution is. Even for more complex choices you could describe the possible outcomes with a measure (probability), which makes it into a law, which in the end reduces free will to just complex coin flipping whose odds depend on your past experience. In what way is this free will? I can only relate to the kind of free will that is defined under compatibilism, which is significantly different from the "original" meaning of free will.

Answer 4

Of course free will works outside the laws of physics. Decision-making is not at all about physics.

The probability of an individual choosing right over left is probably more than 50%. Right-handed people may be more likely to choose right. In some languages right has a more positive feeling to it than left (~wrong). In such a test setup people have no better reasons to choose either way.

Anyway, the people's decisions are not driven by any fixed percentage value. The percentage value reflects the people's choices.