Pettit really only addresses it tangentially, but I like what he has to say about free will in Republicanism:
Whatever existentialists may have thought, individual autonomy or self-rule cannot conceivably require that people should have considered and endorsed each of their particular beliefs and desires in a historical process of self-construction; if it did, then no one would be autonomous. What it requires, more plausibly, is that people are capable of exposing each of their beliefs and desires to appropriate tests, especially in the event of problems arising, and that whether or not they maintain such a commitment depends on how it fares in the tests.
This is something he evidently explores in more detail in a couple essays co-written with Michael Smith, called “Backgrounding Desire” and “Freedom in Thought and Action.” I’ll have to read both of those before making a final ruling, but my initial response is to say that both Pettit and the existentialists are correct: the existentialists have the correct standard for full and true autonomy, but Pettit is right to call this an unachievable ideal and craft a more reasonable alternative.
That said, meeting Pettit’s criteria of autonomy still seems pretty damn hard. I’m not sure if he would make this argument, but I think you could fairly contend that one of the greatest threats to the version of autonomy outlined above is what Heidegger would call “failling”: the ever-present urge to just do what you do and believe what you believe reflexively, without ever self-consciously challenging it. To make full use of Pettit’s version of self-rule — which is to say, to expose each of your beliefs and desires to “appropriate tests” — demands constant vigilance and a willingness to self-criticize without mercy. I’d argue that it’s everyone’s obligation to at least make the effort, but I also acknowledge that it’s a total bitch and I fail at it myself pretty regularly.