In my recent paper Moral Responsibility and Choice I outlined my position that moral responsibility is a result not of actions but of choices. In that paper I deliberately avoided discussing determinism and compatibilism, however I believe the link is clear.
One of the key compatibilist arguments is to reframe the Principle of Alternate Possibilities (PAP) to say that one is morally responsible for an action if one could have done otherwise if one had chosen to do so. Hence the responsibility is shifted from the individual to the environment and the restrictions it imposes. Predicating moral responsibility on the choice rather than the action eliminates this argument and returns responsibility to the individual. The question is no longer if one had chosen differently but if one could have chosen differently. Whether or not one would have been able to follow through with that choice is irrelevant to moral responsibility.
So is choice possible in a deterministic universe? That depends on the definition of ‘choice’. However in the sense I use it in my paper, choice is different from mere selection. A ball on a spinning roulette wheel can land on any of the numbers. Which number it lands on is a selection, not a choice. That is true whether or not the selected number is predetermined (strong determinism) or random (stochastic determinism). The wheel, the ball and the combined system make a selection but do not have a choice.
What if I pick up the ball and place it on one of the numbers on the wheel? Is that a mere selection or a choice? Under either strong determinism or stochastic determinism, my action is merely a selection. I may believe I have a choice, but the mental state I perceive as a decision is as predetermined as the where the ball on the spinning wheel ends up. Belief in having choice is not the same as having choice. My ‘choice’ actually is a deterministic selection between mental states that then leads deterministically to me placing the ball on the selected number.
Choice requires some additional element beyond either determinism or randomness. It requires some form of agent/immanent causation which is not itself subject to deterministic laws.
So moral responsibility requires choice and determinism prohibits choice. Hence determinism is incompatible with moral responsibility.