That means that society does not believe in either non-deterministic incompatibilism (although indeterminism does not entail free will) or compatibilism, then deterministic incompatibilism remains, you may be interested in the opinion of Derk Pereboom:
If quantum theory is true, the position and momentum of
micro-particles exhibit randomness in this same sense, and natural
indeterminacy of this sort might also be conceived as the metaphysical
foundation of indeterministically free action. But natural
indeterminacies of these types cannot, by themselves, account for
freedom of the sort required for moral responsibility. As has often
been pointed out, such random physical events are no more within our
control than are causally determined physical events, and thus, we can
no more be morally responsible for them than, in the indeterminist
opinion, we can be for events that are causally determined.
The hard determinist might deny that at the moment of choice, one must
assume that more than one option is causally possible. One might
instead believe that one’s actions are determined by way of one’s
choices, that one’s choices are determined by means of one’s
deliberation, and that one does not know in advance of deliberation
which action one will choose. As long as one’s actions are determined
by deliberation and choice, and one does not know beforehand what the
result of one’s deliberation will be, there will be no interference
with the deliberative process. Indeed, the deliberative process might
be jeopardized if one had previous knowledge of the choice that would
result. Perhaps it is even incoherent to suppose that one might know
in advance of deliberation which of two roads one will choose, for in
such a situation genuine deliberation would be undermined. But given
that one cannot know the results of one’s deliberation in advance, the
process can go on unimpeded.
Someone might argue that even if no one ever deserves blame, it would
nevertheless be best for us to think and act as if people sometimes
do, because thinking and acting this way is a superb method for
promoting moral reform and education. More generally, even if no one
is ever really morally responsible, it would still be best sometimes
to hold people morally responsible. Such a view might be justified on
practical grounds, were we confident, for example, that thinking and
acting as if people sometimes deserve blame is often necessary for
effectively promoting moral reform and education. But this option
would have the hard determinist thinking that someone deserves blame
when she also believes him not to, which is an instance of theoretical
irrationality, and would have her blaming someone when he does not
deserve to be blamed, which would seem to be morally wrong.
There is, however, an alternative practice for promoting moral reform
and education which would suffer neither from irrationality nor
apparent immorality. Instead of blaming people, the determinist might
appeal to the practice of moral admonishment and encouragement. One
might, for example, explain to an offender that what he did was wrong,
and then encourage him to refrain from performing similar actions in
the future. One need not, in addition, blame him for what he has done.
The hard determinist can maintain that by admonishing and encouraging
a wrongdoer one might communicate a sense of what is right, and a
respect for persons, and that these attitudes can lead to salutary
change. Hence, one need not hold the wrongdoer morally responsible for
what he has done, but rather consider him responsive to moral
admonishment and encouragement. Likewise, although one could not
justifiably think of one’s own wrongful actions as deserving of blame,
one could legitimately regard them as wrongful, and thereby admonish
oneself, and resolve to refrain from similar actions in the future.
But like blame of others, blame of self, and more generally, holding
oneself morally responsible, would be best avoided.
If the hard determinist were to acknowledge that a determinist
conviction could affect the reactive attitudes, but that adopting an
objectivity of attitude would be practically irrational in virtue of
being destructive to human relationships, she might well override
theoretical rationality by retaining her normal reactive attitudes. If
she acted in this way, however, she would be reduced to the
uncomfortable position of maintaining attitudes that are theoretically
irrational. But the hard determinist is not clearly forced into such a
difficult situation. For first, although many ordinary reactive
attitudes might be irrational, these reactive attitudes are not
obviously required for good interpersonal relationships. Some reactive
attitudes, like certain kinds of anger and resentment, may well not be
good for relationships at all. And secondly, the reactive attitudes
one would want to retain have analogues that do not have false
presuppositions. Such analogues by no means amount to Strawson’s
objectivity of attitude, and they are sufficient to sustain good
interpersonal relationships.
References: Pereboom, D. (2009). Free Will (2nd ed.). Hackett Publishing Company, Inc.
And since there is a close relation of necessity between moral responsibility and free will, then you may also be interested in Skepticism About Moral Responsibility:
Skepticism about moral responsibility, or what is more commonly
referred to as moral responsibility skepticism, refers to a family of
views that all take seriously the possibility that human beings are
never morally responsible for their actions in a particular but
pervasive sense. This sense is typically set apart by the notion of
basic desert and is defined in terms of the control in action needed
for an agent to be truly deserving of blame and praise. Some moral
responsibility skeptics wholly reject this notion of moral
responsibility because they believe it to be incoherent or impossible.
Others maintain that, though possible, our best philosophical and
scientific theories about the world provide strong and compelling
reasons for adopting skepticism about moral responsibility. What all
varieties of moral responsibility skepticism share, however, is the
belief that the justification needed to ground basic desert moral
responsibility and the practices associated with it—such as
backward-looking praise and blame, punishment and reward (including
retributive punishment), and the reactive attitudes of resentment and
indignation—is not met. Versions of moral responsibility skepticism
have historically been defended by Spinoza, Voltaire, Diderot,
d’Holbach, Priestley, Schopenhauer, Nietzsche, Clarence Darrow, B.F.
Skinner, and Paul Edwards, and more recently by Galen Strawson, Derk
Pereboom, Bruce Waller, Neil Levy, Tamler Sommers, and Gregg D.
Caruso.
And more specifically, since disbelief in free will generally entails disbelief in moral responsibility, see Implications of Moral Responsibility Skepticism:
Turning now to the practical implications of moral responsibility
skepticism, we can ask, what would happen if we came to accept this
view? In recent years a small industry has grown up around precisely
this question. Since disbelief in moral responsibility would clearly
have profound consequences for our interpersonal relationships,
society, morality, meaning, and the law, it’s important to question
whether these consequences would be (on the whole) good or bad.
Critics of moral responsibility skepticism fear that it would
undermine morality, leave us unable to adequately deal with criminal
behavior, increase anti-social conduct, and/or destroy meaning in
life. Moral responsibility skeptics, on the other hand, offer up a
number of different views—including illusionism (Smilansky 1999,
2000), disillusionism (Nadelhoffer 2011), and optimistic skepticism
(e.g., Spinoza 1677 [1985]; Pereboom 1995, 2001, 2002b, 2009, 2011,
2013a, 2014a; Waller 1989, 1990, 2004, 2006, 2011, 2014; Sommers
2007a,b; Caruso forthcoming-b; N. Levy 2011; Vilhauer 2009a,b, 2012,
2013a,b; Milam 2016, 2017; Smuts 2014; Morris, forthcoming).
