The approach suggested here is intellectually more modest and realistic, without sacrificing generality. It does not regard uncertainty as an aberrational exogenous disturbance, as does the usual approach from the opposite extreme of accurate foresight. The existence of uncertainty and incomplete information is the foundation of the suggested type of analysis; the importance of the concept of a class of "chance" decisions rests upon it; it permits of various conflicting objectives; it motivates and rationalizes a type of adaptive imitative behavior; yet it does not destroy the basis of prediction, explanation, or diagnosis. It does not base its aggregate description on individual optimal action; yet it is capable of incorporating such activity where justified. The formalization of this approach awaits the marriage of the theory of stochastic processes and economics-two fields of thought admirably suited for union. It is conjectured that the suggested modification is applicable to a wide class of events and is worth attempts at empirical verification.''“N17 (emphasis added)
Note 17: "Preliminary study in this direction has been very convincing, and, in addition, the suggested approach appears to contain important implications relative to general economic policy; but discussions of these are reserved for a later date. Alchian ((1950) “Uncertainty, Evolution, and Economic Theory,” 221; emphases added)
Alchian’s approach turns on three crucial steps: first, one brings uncertainty within one’s formal apparatus by, second, treating Knightian uncertainty essentially as an instance of randomness. Third one then treats randomness as a stochastic process (recall this post).
Alchian’s move, in turn, has two far-reaching pay-offs: first, by treating Knightian uncertainty as something that can be put inside the model by substituting randomness for it, one can use mathematical technique(s) (e.g., Monte Carlo simulations, Kolmogorov randomness, martingales, etc.) to assign numbers where that previously had been impossible. Once Knightian uncertainty is reinterpreted as a stochastic process and after specifying the mathematical technique by which one models randomness, it can be domesticated within a formal framework. Second, such a formal framework holds the promise in Alchian’s words of “empirical verification.”As I noted before, Alchian's move got picked up by Arrow at once, and it was incorporated not just into general equilbrium theory, but also became a corner-stone of portfolio-theory, finance, and option pricing. Eventually, Alchian's move became central to the very idea of (financial) markets, which came to be understood as random walks (with no arbitrage).
Alchian’s paper is explicitly acknowledged in the very first note of Gary Becker’s seminal, “Irrational Behavior and Economic Theory” (1962). As Foucault rightly notes, Becker’s position can be understood as claiming that “rational conduct is any conduct which is sensitive to modifications in the variables of the environment and which responds to this in a non-random way, in a systematic way.” (Foucault The birth of biopolitics, p. 269. Unfortunately, in his footnotes Foucault refers incorrectly to the title of Becker’s paper!)
One might think given Foucault's use of 'non-random' that Becker's approach differs from Alchian's in a non-trivial way. But that's not quite right. Because, in a rare oversight, Foucault seems to be unaware of Alchian, he misses Becker's claim that "impulsive behavior will be represented by a probabilistic model in which decisions are determined so to speak, by the throw of a multisided die." (Becker, 5; the whole page is relevant.) So we need to restate Foucault's claim about economics as follows, “rational conduct is any conduct which is sensitive to modifications in the variables of the environment and which responds to this in a systematic way even if the individual's [firm's, etc.] decision rule appears to be random.” This is, as Foucault correctly recognized, a non-trivial departure from Savage's axioms (as an aside, Savage may have recognized the possibility, and we should be surrpised he understood his own approach to be normative not empirical long before it was fashionable (20ff)).