Risk Versus Uncertainty
This is the 3rd of a series of 9 posts on Foundations of Probability. This continues from previous post (Three Types of Probability) . Section 2 of the paper “Subjective Probability Does Not Exist“ is entitled “Risk Versus Uncertainty”, and explains how a (false) technical argument, which continues to be widely accepted and believed, banished uncertainty from the world, and replaced it by risk.
Section 2: Risk Versus Uncertainty.
“… the race is not always to the swift, nor the battle to the strong …” Ecclesiastes 9:11
In this section, we recapitulate an intellectual battle about the nature of probability which took place in the early twentieth century, which was won by the wrong side, due to these confusions over the nature of probability. This victory has been enormously influential in shaping modern economic and financial theory. As Keynes recognized “The ideas of economists and political philosophers, both when they are right and when they are wrong are more powerful than is commonly understood. Indeed, the world is ruled by little else.” Wrong ideas about probability rule the world today. These ideas led to a false assurance about the predictability of the future, and left economists unprepared for the Global Financial Crisis. These ideas continue to dominate the theoretical discourse, especially in economics, with disastrous consequences.
All of social science must be grounded in theories of human behavior. Human decisions are generally directed towards the future. I take action A because I expect good consequences will occur due to my action. Investors invest based on expectations regarding economic prospects about the future. Firms make decisions to produce based on expectations regarding how much they expect to be able to sell, and at what prices, in the future. Recognition of the central role of probability in our daily decisions led the aphorism “Probability is the very guide to life”. In particular, decision making under uncertainty is at the heart of economic theory. Uncertainty reflects lack of knowledge about what might happen in the future. There are several different levels of knowledge about the future, which need to be distinguished.
Certainty: This holds when the future is exactly known, deterministically.
Risk: This holds when we can predict the pattern of the outcomes. To be more precise, there is a fixed and finite number of outcomes E1, E2, …, En which may occur. Decision makers, referred to as agents subsequently, know the events and also knows their ontic or epistemic probabilities of occurrence p1, p2, …, pn.
Mild Uncertainty: There is a fixed and finite number of events E1,…,En but agent A does not know their ontic or epistemic probabilities. To make decisions, agents must acquire relevant knowledge regarding the past historical record, or the circumstances which create these outcomes, and transform this knowledge into an epistemic probability, which represents their best guess at the ontic probabilities.
Radical Uncertainty: The range of events which may occur is large and unknown, and the agent A has insufficient knowledge to allow for a guess at the ontic probabilities of these events.
Traditional economic theory assumes complete certainty about the future to derive decisions of consumers and firms. This theory can be extended to situations of risk, when all agents know the probabilities of outcomes of all possible economically relevant events. The theory breaks down under conditions of mild uncertainty, since decision makers cannot even calculate the expected values of the consequences of their actions. This makes the optimization decisions at the heart of economic theory impossible. Even worse is the case of radical uncertainty. Here, even the range of actions open to agents is not known, and innovators can come up with new ideas and actions which are not within the range of possibilities imagined by others. With this terminology in place, we can describe the intellectual battle as follows. Keynes (1921) and Knight (1921) argued the radical uncertainty is ubiquitous in economic environments. It is this uncertainty which created profit opportunities, according to Knight. In Keynesian theory, investors beliefs were based on “animal spirits” (recently renamed as “irrational exuberance”), because of the fundamental uncertainty surrounding the future. The concept of profit maximization for firms does not make sense when future consequences of current production decisions cannot be foreseen. In particular, future prices are unknown and unknowable. However, Ramsey and De-Finetti came up with a technical argument which appears to show that all situations of uncertainty can be reduced to risk. Rational decision makers facing uncertainty will assign probabilities to all uncertain events, thereby reducing uncertainty to risk. Thus, mild or radical uncertainty does not exist for rational agents.
John Kay (2019) writes the “It is difficult to exaggerate the practical consequence of the outcome of that technical argument. To acknowledge the role of radical uncertainty is to knock away the foundations of finance theory and much modern macroeconomics. But the reigning consensus (that uncertainty does not exist) is beset with glaring weaknesses. Keynes and Knight were right, and their opponents wrong. And recognition of that is a necessary preliminary to the rebuilding of a more relevant economic theory.” It is the central goal of this paper to explain why the reigning consensus, which banishes both mild and radical uncertainty from economic theory, is wrong.
In order to explain its glaring weaknesses, we will replicate the argument of Ramsey, De-Finetti and Savage in the simplest possible context, stripped of all extraneous complications. The basic argument establishes the existence of revealed probability in certain decision-making contexts. There are two mistakes in the arguments for subjective probability, both based on logical positivism. One mistake is the rejection of ontic probabilities, and the second is the rejection of epistemic probabilities. Both of these are unobservable, and hence, meaningless concepts, according to extreme positivists. The empiricism which leads to the denial of meaning to concepts of ontic and epistemic probabilities is the key to the victory of Ramsey and de-Finetti over Keynes and Knight, and also the key to the persistence of this error for nearly a century.
Next Post: Section 3: Blinders of Empiricism (Part 1) (4/10)