Popper wrote extensively on the problem of determinism and free will, researched many earlier thinkers on the subject, and formulated his own "evolutionary" model of free will. In his Arthur Holly Compton lecture, Of Clouds and Clocks, delivered at Washington University in St. Louis in April 1965, he noted that earlier thinkers had seen the only alternative to determinism as chance. This is the classic argument against free will, that it comes to a stark choice between determinism or indeterminism. Hume found nothing between chance and necessity, and Eddington had said, there is "no halfway house" between randomness and determinism. But note that Popper may have been inspired by Arthur Holly Compton himself, who said an "act of choice [adds] a factor not supplied by the physical conditions...determining what will occur." See Compton's Atlantic Monthly article. In his dialogues with John Eccles, (The Self and Its Brain, 1977), at first Popper dismissed quantum mechanics as being no help with free will, but later describes a two-stage model that parallels Darwinian evolution, with genetic mutations being probabilistic and involving quantum uncertainty.
Popper replying to John Eccles:
"First of all, I do of course agree that quantum theoretical indeterminacy in a sense cannot help, because this leads merely to probabilistic laws, and we do not wish to say that such things as free decisions are just probabilistic affairs. "The trouble with quantum mechanical indeterminacy is twofold. First, it is probabilistic, and this doesn't help us much with the free-will problem, which is not just a chance affair. Second, it only gives us indeterminism, not openness to World 2 [Popper's Mind World]. However, in a roundabout way I do think that one may make use of quantum theoretical indeterminacy without committing oneself to the thesis that free-will decisions are probabilistic affairs.Here Popper compares new ideas to variation in the gene pool due to random mutations followed by natural selection, as William James had done in 1880.
"New ideas have a striking similarity to genetic mutations. Now, let us look for a moment at genetic mutations. Mutations are, it seems, brought about by quantum theoretical indeterminacy (including radiation effects). Accordingly, they are also probabilistic and not in themselves originally selected or adequate, but on them there subsequently operates natural selection which eliminates inappropriate mutations. Now we could conceive of a similar process with respect to new ideas and to free-will decisions, and similar things.
A few years earlier, Popper had called for a combination of randomness and control to explain freedom, though not yet explicitly, as is needed, in two stages with random chance before a controlled decision.
"freedom is not just chance but, rather, the result of a subtle interplay between something almost random or haphazard, and something like a restrictive or selective control" (Objective Knowledge, Of Clouds and Clocks, 1972, p. 232)
For those extreme libertarians who prefer a traditional definition of freedom as pure chance (liberum arbitrium indifferentiae), we can offer free will as Popper's interplay between chance and control. In 1977 Popper gave the first Darwin Lecture, at Darwin College, Cambridge. He called it Natural Selection and the Emergence of Mind. In it he said he had changed his mind (a rare admission by a philosopher) about two things. First he now thought that natural selection was not a "tautology" that made it an unfalsifiable theory. Second, he had come to accept the random variation and selection of ideas as a model of free will.
The selection of a kind of behavior out of a randomly offered repertoire may be an act of choice, even an act of free will. I am an indeterminist; and in discussing indeterminism I have often regretfully pointed out that quantum indeterminacy does not seem to help us;1 for the amplification of something like, say, radioactive disintegration processes would not lead to human action or even animal action, but only to random movements. I have changed my mind on this issue.2 A choice process may be a selection process, and the selection may be from some repertoire of random events, without being random in its turn. This seems to me to offer a promising solution to one of our most vexing problems, and one by downward causation.