Uncertainty vs Risk vs Randomness vs Risk

During the last two weeks I was immersed in Ghislaine Idabouk's briliant dissertation on the mathematics of options pricing (Black, Scholes, Merton, etc). She passed her Viva with flying colors and all of us encouraged her to translate it into English and expand it in order to publish it as a monograph. Ghislaine's dissertation has inspired me to start a weekly regular column on contemporary philosophy of economics (on Tuesdays).

Ghislaine's dissertation nicely brings out how many of the assumptions behind the mathematical structure of finance theory borrows  (and interestingly re-orients it away) from the core of post WWII economic theory. This core is derived from work done by Arrow and Samuelson. (Other names, Debreu, of course, could also be mentioned.) It is worth emphasizing this because in recent (reasonably intellectual) public discussions and polemics about economics, Keynes, Friedman, and Hayek all figure more prominently. This is why I was so delighted by Paul Krugman's recent colum (initially discussed on this blog here), where Samuelson's legacy is singled out. There is much to say about Krugman's view on it (and his views on why the legacy was "unstable"). But here I am going to focus on a bedrock assumption within the Arrow/Samuelson legacy, one of the crucial steps to make economics a science useful to technocrats: the reformulation of uncertainty as randomness.

In 1921, Frank Knight published Risk, Uncertainty and Profit. In it he draw a sharp contrast (quoting from wikipedia now:) "situations with risk were those where decision making was made faced with unknown outcomes but known ex-ante probability distributions. He argued that these situations, where decision making rules such as maximising expected utility can be applied, differ in a deep way from those where the probability distribution of a random outcome is unknown." The wikipedia summary is excellent, except that a bit of anachronism slips in at the very end--namely the equation of uncertainty with randomness. But this equation between uncertainty and randomness is the hard fought result of Arrow's and (more tacitly) Samuelson's attack on the very idea of uncertainty, which in its original version ruled out that one could assign a number to some decision procedure. That is to say, if one can define uncertainty away as randomness it can not only become a sub-species of risk, but it can then also allow the economist to generate a decision procedure (e.g., a monte carlo simulation) which "tracks" it. Moreover, as Ghislaine's dissertation reveals nicely, systems that exhibit randomness can have well known mathematical properties (think of Brownian motion).

Interestingly enough, one of the best known papers in decision theory, Ellsberg's "Risk, Ambiguity, and the Savage Axioms," self-consciously resists the Arrow-Samuelson move (see the remarkable first page and footnote, where Arrow's criticism of Knight is quoted in part), argues (conclusively?--he has a paradox named after him!) that there are other sources of uncertainty that are unrelated to randomness. Yet, mainstream economic theory ignored Ellsberg. (At a later date I will call attention to Malinvaud's subtle criticism that makes a related point on uncertainty.)

Why does this matter? Here's one reason: the Arrow-Samuelson move (uncertainty = randomness) made it possible to think of economics as an exact policy science that could prove *determinate* policy advice. It made economics, thus, safe for technocracy. But if policy decisions are fundamentally uncertain, then other principles come into play. For example, if uncertainty is allowed back in then precautionary principles ought to become a much larger element of the economists' tool-kit.