Often when free will is discussed, there are three main positions espoused:
Libertarian: The universe is not deterministic and there is free will
Hard-determinism: The universe is deterministic and there is no free will
Compatibilism: The universe is deterministic and there is free will
There seems to be an obvious missing category. I don't think it would simply be a matter of semantics, or unnecessary filling of a gap to include it. I think it's a sensible position to hold.
Suppose you were about to perform an action and there is a set of possible actions, more than one, that you can possibly perform. That set of possibilities has an underlying probability distribution. This would imply that the universe is not deterministic. It's possible that this probability distribution is governed by nature. In principle, given all the information about the current state of things, including the supposed agent, you could calculate the probability distribution over that agent's choices. If the probability distribution of the agent's choices is determined by nature, and not the agent, then, in a similar manner to the hard determinist line of thinking, you could argue that the agent is not free.
Is there a term for the position that nature is not deterministic, but there is still no free will? Is it similar enough to hard determinism that it need not have its own category? And does this position get argued often in philosophy?