Alchian’s move, in turn, has three far-reaching pay-offs (two of which explicitly noted by him in his article): 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.” Third, it opens the door to treating formal approaches and economics more generally as relevant to “economic policy.” This allows economists to market their skills to policy-makers as technical specialists without constantly offering disclaimers.
Now, this sophisticated displacement strategy is quite clever. For, it transforms an epistemic doctrine (which Alchian treats as the opposite of “accurate foresight”) into a metaphysical claim: the existence of “chance decisions.” This is why he can assert the “existence of uncertainty” within the proposed model-world. And these decisions are now modeled as a sequence of random events. It turns Keynes’ argument for ersatz-risk, which for the sake of action pretends as if metaphysical uncertainty does not exist, on its head! For, as Arrow had noted when he called attention to Alchian’s approach, according to Alchian if we assume that we must act then we might as well treat each act as (or as-if) a step in a random sequence. Knightian estimates suitable for ordinary life get replaced by random sequence(s). Moreover, as Arrow had realized, such a sequence will produce optimizing or rational outcomes without assuming rational agency from the start.
This is, in effect, the high level conceptual blue-print for turning random walks in, say, market prices into efficient markets. The crucial steps are taken by Alchian’s (Nobel-prize winning) student, William F. Sharpe (1964)“A Theory of Market Equilibrium under Conditions of Risk”, and Paul A. Samuelson (1965) "Proof That Properly Anticipated Prices Fluctuate Randomly,", which treats the market as a fair game and a stochastic process. Fellow Tufts alumnus, Eugene Fama, who synthesized these ideas in a classic article, must wonder why the Nobel committee did not reward him when these ideas were still fashionable.
That is, Alchian’s approach is a brilliant way of operationalizing one’s ignorance (cf. also the importance of “imperfect information” in Alchian above). It offers the lure of making epistemic versions of uncertainty tractable (without pretending that people walk around with consistent probability measures). But metaphysically there is a huge difference between treating the world as a stochastic process (randomness) and treating it as indeterminate (uncertainty). To oversimplify the difference: treating the world as stochastic encourages the idea that one take controlled bets on outcomes, while treating it as indeterminate means one recognizes one has no grip at all on underlying distributions.
Alchian’s sophisticated displacement strategy anticipates the way how mathematical techniques such as Ito’s lemma or semi-martingales got incorporated into finance-theory (Black-Scholes, etc). (Recall how Idabouk's dissertation got me interested in this issue.) These techniques treat the world as a random, albeit fair game and, thus, incorporate assumptions about which distributions are possible and which are not. Such techniques put constraints on what’s possible as a consequence of the adopted formalism; they are very sensitive to assumptions about distributions. There is a related problem which has been pressed in prominent recent writings on finance thory: the so-called “ludic fallacy” a term coined by Nassim Nicholas Taleb in his 2007 The Black Swan. It turns on the misuse of games to model real-life situations. (Recall my discussion here.) However, we need to distinguish between the ludic fallacy and between the assimilation of metaphysical uncertainty to statistical processes. The former is a sub-set of the latter.
So, a concept which had been explicitly introduced to resist formalization, “uncertainty,” became tamed in various formal frameworks. While the simple displacement strategy (treat uncertainty as probable risk or subjective probability) simply wished uncertainty away, the sophisticated displacement strategy cleverly offers a way of operationalizing agents’ ignorance. But the mathematical treatments of randomness preferred in economics and finance are metaphysically not innocent. They make commitments about underlying distributions and modalities that are not warranted when one accepts genuine uncertainty. The proponents of formalization have rightly insisted on the clarity which mathematical treatments can provide. But in re-reading the mathematical economists' strategies for displacing uncertainty, I have found boundless optimism about available formal techniques for the purpose of modeling, and over-eagerness in assuming away the unknown, unknowns. One never encounters statements of caution; rather one finds ridicule of folk that resist formalization. While the philosopher in me would like to think that certain questions would have been asked by philosophic minds (and it is worth noting that Keynes, Knight, Hayek, Shackle, and more recently Taleb never severed the link between philosophy and economics), one should also not be blind to the financial and political incentives that would motivate over-confidence in certain mathematical techniques. Not to mention the sad fact that philosophical decision-theorists have been cheer-leaders for the neglect of genuine uncertainty. Society is paying a heavy price for the economists’ overconfidence.