The Probability Increase Thesis* (PIT): If it is indeterminate whether S will make a choice C, and C occurs, then S is morally responsible for C only if the probability of C given S’s choice is greater than the probability of C given the antecedent conditions.
Does this sound plausible?
Consider the following cases:
S1: Smith pops into existence, and begins deliberating whether to kill Jones or not kill him. At t1, just prior to choosing, Smith is 80% disposed (for whatever reasons) to choose to kill Jones, and there are no other mitigating factors so that the total probability is .8 that Smith will choose to kill.  Smith chooses (at t2) to kill. So Smith raises the probability of his choosing to kill from .8 to 1.0. Thus, he bears at least some moral responsibility according to PIT.
S2: Smith pops into existence, and begins deliberating whether or not to kill Jones. At t0, in the course of Smith’s deliberation, Black introduces a neural process P into Smith’s brain that will deterministically result in his choosing (at t2) to kill Jones. Thus, at t1, the probability is 1.0 that Smith will choose to kill Jones. At t2, Smith chooses to kill Jones (whether on his own or as a result of P), but he does not raise the probability that he will choose, since it was already 1.0. Thus, Smith is not responsible for choosing to kill Jones according to PIT.
S3: A scenario just like S2, except that Smith makes choices prior to t0 that raise the probability of his choosing to kill from the initial .8 to .9. Black then initiates P, and the probability goes to 1.0. Is Smith morally responsible for his choice accoring to PIT?
* This idea is adapted from Peter Vallentyne’s paper “Brute Luck and Responsibility,” Politics, Philosophy & Economics 7 (2008): 57-80. I have modified it a bit, but if PIT is any good at all, Vallentyne gets the credit.