2.1Before the dispute: two faces of probability
The quarrel over Knight is older than Knight. Hacking (1975) traces the concept of probability to around 1660 and finds it with two faces from the start: the frequency of chance events, and the degree of belief that evidence warrants. Daston (1988) follows probability through the eighteenth century as a model of reasonable judgment, used among other things in insurance and annuities. Both histories matter here because Knight's two kinds of uncertainty can be mapped, loosely, onto Hacking's two faces. Risk, in Knight's sense, is the frequency face made usable: a known proportion of outcomes in a group of cases. Uncertainty sits nearer the face of belief, since what remains when no group can be formed is an opinion and the decider's confidence in it.
The mapping is loose because Knight himself did not let the two faces fall apart cleanly, as Section 4 shows. He held that even an estimate can be grouped, given enough estimates by the same person, and that the line between a statistical probability and an estimate is a matter of degree. That is the point at which the later readings divide.
Keynes's Treatise (1921) adds a third consideration. Probability, for Keynes, is a logical relation between evidence and conclusion, and not always a number. This article draws from that the consequence that a decider can hold a probability without being able to state it as a ratio. Keynes also separates the weight of the evidence from the probability it supports: two judgments can have the same probability and rest on very different amounts of evidence. Both points bear on any record that asks a decider to report a confidence. A number reported does not show how much evidence lies behind it.
2.2The market reading
LeRoy and Singell (1987) offer a reading of Knight centred on insurance. On their reading, Knight's line between risk and uncertainty does not turn on whether people can form probabilities, since, they argue, Knight took subjective probabilities for granted. It turns on whether an insurance market for the risk can exist. Uncertainty, for them, is where moral hazard and adverse selection keep a risk from being insured. In the usual senses of the terms, moral hazard is the change in conduct of a party whose losses another bears, and adverse selection is the tendency of those who know themselves to be bad risks to seek cover most.
The strength of this reading is that it makes Knight's distinction an institutional fact that can be checked: either a market exists for a given hazard or it does not. Its cost is that it moves the source of uncertainty out of the decider's head and into the relations between the decider and others.
2.3The classing reading
Langlois and Cosgel (1993) answer LeRoy and Singell. For Knight, they argue, uncertainty arises where instances cannot be sorted into classes of like cases. Where no class can be formed, no frequency can be had, and the situation calls for judgment. That judgment, the entrepreneur's, is what the firm is built around.
The strength of this reading is its fit with the long epistemological chapter that precedes Knight's naming of the two kinds, Chapter VII, where classification is the central idea. Its cost is that it makes the distinction depend on something hard to observe from outside: whether a given case can be classed with others is partly a matter of how the decider and the observer choose to describe it.
2.4The two readings side by side
| Market reading (LeRoy and Singell 1987) | Classing reading (Langlois and Cosgel 1993) | |
|---|---|---|
| What makes a hazard uncertain | No insurance market can exist for it | Its instances cannot be sorted into classes of like cases |
| Can the decider form a probability? | Yes; Knight took subjective probabilities for granted | No frequency can be had; judgment is called for |
| Mechanism named | Moral hazard and adverse selection | Absence of a class |
| Where the difficulty lives | Between the decider and those who might bear the risk | In the case and its description |
| What follows | Uninsurable risk | Judgment, around which the firm is built |
The table shows two answers to one question. It also shows that the two answers need not exclude each other. A hazard could be unclassifiable and, for that reason, uninsurable; or it could be classifiable in principle and still uninsurable because those who would bear it cannot watch the person who decides. Section 6 argues that Knight's own Chapter VIII puts both reasons into a single passage.
2.5Experiment and after
Ellsberg (1961) gave Knight's distinction an experimental form. People prefer a bet whose odds are known to an otherwise equal bet whose odds are unknown, a preference now called ambiguity aversion, and the pattern of choice breaks Savage's axioms of subjective expected utility. How the result bears on the two readings of Knight is this article's own placement. On the market reading, it matters because the subjective probability the reading takes for granted does not behave like a known frequency. On the classing reading, it matters because an urn of unknown composition is the simplest image of a case with no class: the decider knows what can happen but not in what proportion.
Kay and King (2020) widen the point. Many decisions, they argue, face a radical uncertainty that probabilities cannot capture, and they recommend asking what is happening in the situation at hand, reasoning with narratives, and choosing strategies that are robust and resilient to what cannot be foreseen, rather than optimising on invented numbers. Their book is cited here because one of the two records below adopts something close to their advice: it gives one part of a decision a narrative role and another part a rule.
2.6What both readings leave aside: the time of the writing
A third body of work, concerned with forecasts and stakes rather than with Knight, sets the scene for the records. Brier (1950) proposed a score for probability forecasts, the mean squared difference between forecast probabilities and what happened, which a forecaster cannot improve by stating anything but the probability believed. Tetlock (2005), in a long study of expert forecasts on political and economic questions, found the experts poorly calibrated, often no better than simple rules, with those who drew on many ideas and revised readily doing better than those committed to one big idea. Kelly (1956) showed that a gambler with a private source of information maximises the long-run growth of capital by staking a fraction set by the edge, and that staking more than that fraction lowers long-run growth and raises the risk of ruin. Jensen and Meckling (1976) set out the agency costs that arise when one party acts for another: monitoring, bonding, and the loss that remains.
None of these works is cited here as a reading of Knight. What this article takes from them is that each, as described above, works on a record kept over time: forecasts against outcomes, stakes against returns, an agent's conduct against the monitoring of it. That is the element both readings of Knight leave in the background. The market reading asks whether a market can exist; the classing reading asks whether a class can exist. Neither asks when the class comes into existence, or who writes the description that puts a case in it. The records below are documents in which that writing happens.