Free Will as Precision Control: A Bayesian Take

A Bayesian argument for compatibilism

I used to think free will was a lie. We’re all just automatons following mathematical rules. Nobody ever really “decides” anything.

That way of thinking made me miserable. Rather than let my life continue to fall apart - despite that being what the evidence told me was most likely - I embraced the concept of free will without understanding it.

Atlas, exercising his mid-anterior cingulate cortex to pin the probability of “I will hold up the world” to 1, with high precision

I could tell believing I made choices worked for me, but I’ve long wanted to understand why. Predictive processing seemed to point in the direction of “you can get evidence that you can complete goals, and this evidence grows exponentially.” I’ve never laid that argument out in detail, because I still couldn’t see how that worked precisely, in the moment. How do you go from zero to one? If you’ve got no great evidence that you’ll ever stop using drugs - because all your prior attempts have failed - how can you generate that first bit of evidence that yes, you can?

I’ve got a hunch, now, and want your help to evolve it.

Imagine your cortex as a network of little statisticians, constantly making guesses about the world and then checking those guesses against what actually happens. Every time you touch a hot stove or talk to a friend, your neurons update their priors a tiny bit. Prediction errors roll in from the bottom up, top-down signals try to explain them away. Life is just a Bayesian dance, but there’s no ‘you’ dancing here - just atoms raving in the void.

If that’s all there is, free will seems impossible. Everything you “decide” would just be the posterior probability of acting one way or another. You might think, “I’ll probably eat the salad 40% of the time,” and that probability would just drift up and down as evidence arrives. You would be, in essence, a very sophisticated spreadsheet running on meat.

But here’s the thing I’ve started to notice: sometimes I don’t just let probabilities float around. Sometimes I pin them down and say, “No. I will do this.” That’s what it feels like when I make an intention. “I will act with honesty.” “I will go to the gym.”

I don’t compute the probability of a thing being true, I turn it into a decision variable, effectively forcing it closer to 1.

In Bayesian terms, intention works by cranking up the ‘precision’ of a belief, and tweaking its value. When you set an intention, the brain treats the belief as almost certain, sending signals downstream. Sensory feedback now has to bend reality to match the belief, rather than nudging the belief itself. That creates a feedback loop: intention → action → observation → error correction → intention reinforced. Neuroscientists would recognize this as a form of top-down control, over the precision and value of a given prediction in your belief network.

This is not magic. There’s a physiological story for it. The mid-anterior cingulate cortex seems to be the part of the brain that notices conflicts and decides which errors are worth fighting. When you decide to stick to an intention, it sends a top-down signal, effectively saying, “I’m not listening to the usual evidence right now.” That costs energy. Willpower is metabolically expensive because your brain is basically running a high-precision prior on a short leash, and every bottom-up temptation or doubt is an error it has to suppress.

Once you understand it this way, a few things click. Habits are just low-cost precision control loops: you’ve repeated the action enough times that the top-down priors don’t need much effort to hold. Weak intentions feel exhausting because your posterior is still pulling you one way, and your mACC is burning glucose to resist it. You can even see this in why some people can hold complex, morally charged goals in mind while others can’t—they’re basically allocating precision differently.

So what is free will? It’s not magic, or a miracle. It’s not the absence of causality. It’s control over which parts of your Bayesian machinery get to act as causes rather than effects. You choose the priors that become active levers in the world. That’s all, but that’s enough. The rest of the world—the rest of your brain—just has to catch up.

This process will work only in your proportion to your belief that it does. It’s an evidentiary feedback loop that relies on metabolic energy passing through a specific brain network that can nudge probabilities and precisions. The more evidence you get that this process works, the easier it becomes to use it.

But how do you get started on this if you’re stuck at zero probability that any of this will work?

Being part of a community that says “you can get better” might be what it takes to help people get started. This might be why, among other things, Alcoholics Anonymous and other groups tell people to give up the idea that you can do it, and to instead trust in ‘a higher power’. Hearing other people say, “I tried many times and failed, but finally with the help of this group, I did it,” might help shift your internal probability that you can quit.

Even with that help to shift the value of the prediction, you’ll still need to pin its precision yourself. Or, in other words - once considered obvious, now ‘old fashioned’ - you have to choose. Community can help you - in particular a community that emphasizes the importance of believing in free will and personal responsibility - but you still need to choose.