LESSWRONG
LW

by MichaelA
23 min read
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Overview

We’re often forced to make decisions under conditions of uncertainty. This may be empirical uncertainty (e.g., what is the likelihood that nuclear war would cause human extinction?), moral uncertainty (e.g., does the wellbeing of future generations matter morally?), or one of a number of other types of uncertainty.

But what do we really mean by “uncertainty”?

According to [one] view, certainty has two opposites: risk and uncertainty. In the case of risk, we lack certainty but we have probabilities. In the case of uncertainty, we do not even have probabilities. (Dominic Roser [who argues against this view])

So what are we really talking about - risk, or (Knightian) uncertainty? What is such a distinction meant to mean? Does such a distinction make sense? What significance might this distinction have for how we resolve and make decisions given a lack of certainty? And what about unknown unknowns, black swans, and incomplete models?

These are the questions I discuss in this post, arriving at the following claims:

  1. The risk-uncertainty distinction is usually not adequately specified; it lets a lot of the “work” be done by ambiguous phrases such as whether probabilities are “known” or “exact”.[1]

  2. Proponents of the risk-uncertainty distinction usually seems to discuss it as if it’s an absolute, binary distinction, or fundamental dichotomy; as if in some cases we really do “know” (or “really can estimate”, or whatever) the probabilities of interest, while in other cases we really can’t at all. To be clear, the alternative to this view is the idea that:

    • sometimes we have extremely little basis for estimating probabilities
    • other we times have extremely good basis for estimating probabilities
    • but these situations aren’t fundamentally different
    • there’s a continuum of possibilities in between those extremes
    • (I would obviously agree with the above four points, and thus with the idea of distinguishing between more “risk”-like situations and more “(Knightian) uncertainty”-like situations, along a continuum. This post collects some terms and concepts relevant to this more continuous view.)

  3. That’s a false dichotomy; no absolute, binary distinction can be made.

    • One quick quote to indicate that this view isn’t unique to me: “Bayesian approaches to probability treat it as a degree of belief and thus they do not draw a distinction between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty” (Wikipedia).
    • (This post will essentially presume a Bayesian interpretation of probability, or possibly also argue for it, though I doubt that all the claims I make rely on the Bayesian interpretation.)

  4. Thinking that there is such a binary distinction can lead to using strange and suboptimal decision-making procedures.

This post discusses each of these four claims in turn. I close by considering how unknown unknowns (or black swans, or incomplete models) fit into this picture.

This post doesn’t address the idea that, as a practical or heuristic matter, it might be useful to act as if there’s a risk-uncertainty distinction. My next post will address that idea, and ultimately argue against it.

Epistemic status

The questions covered in this post all subject to substantial debate and have received some good treatments before. (I’d particularly recommend this short post by Ozzie Gooen, this paper by Dominic Roser [behind a paywall, unfortunately], and this series of posts by Nate Soares.) I’m also not an expert on these topics. Thus, this is basically meant as a collection and analysis of existing ideas, not as anything brand new. I’d appreciate feedback or comments in relation to any mistakes, unclear phrasings, etc. (and just in general!).

My three goals in writing this were to:

  • Force me to clarify my own thinking and understandings.
  • Provide an additional primer/resource on these topics, which will hopefully be fairly accessible, will take a different line of attack, and will collect in one place what seem to me to be the most important points. (This is particularly for the sake of those who don't already see the risk-uncertainty distinction as obviously flawed.)
  • Set the scene for a later post, which will discuss essentially the exact same questions, but in the context of moral uncertainty in particular (which does not appear to have been adequately done before).

What’s the distinction meant to mean?

Wikipedia captures the everyday usage of the terms uncertainty and risk:

Uncertainty [is the ] lack of certainty, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome.

[...] Risk [is a] state of uncertainty where some possible outcomes have an undesired effect or significant loss.

However, among some people and in some fields (particularly business and finance), it’s common to make a quite different risk-uncertainty distinction, like the one made in the quote at the beginning of this post. This different risk-uncertainty distinction (which is the one this post will focus on) is not about whether we’re talking about the possibility of something negative.

Instead, this distinction centres on something like whether we can “have”, “know”, “express”, “estimate”, or “quantify” the probabilities of interest (or perhaps, more specifically, “believable”, “justifiable”, or “precise” probabilities). If we can, we’re facing risk (even if the potential outcomes are all positive). If we can’t, we’re facing uncertainty (or Knightian uncertainty).[2]

Here’s one way of explaining this risk-uncertainty distinction:

According to a seminal classification by Knight (1921), three types of uncertainty can be distinguished. In some situations, we can calculate the objective probabilities of events a priori, for instance, the chances of a (fair) die showing a six. In other cases, probabilities can be estimated statistically from data, for instance, the chances of being wrongly diagnosed [with] cancer when participating in regular screenings. Both cases are referred to as situations of risk.

Finally, there are situations with so many unique features that they can hardly be grouped with similar cases, such as the danger resulting from a new type of virus, or the consequences of military intervention in conflict areas. These represent cases of (Knightian) uncertainty where no data are available to estimate objective probabilities. While we may rely on our subjective estimates under such conditions, no objective basis exists by which to judge them (e.g., LeRoy & Singell, 1987). However, even when information is in principle attainable and chances could be estimated, an individual agent or agency may still lack the time or resources to do so—and thus face a situation of uncertainty. (bolding and line break added)

Here’s another similar explanation:

In the case of risk, the outcome is unknown, but the probability distribution governing that outcome is known. Uncertainty, on the other hand, is characterised by both an unknown outcome and an unknown probability distribution. For risk, these chances are taken to be objective, whereas for uncertainty, they are subjective.

Consider betting with a friend by rolling a die. If one rolls at least a four, one wins 30 Euros [...]. If one rolls lower, one loses. If the die is unbiased, one’s decision to accept the bet is taken with the knowledge that one has a 50 per cent chance of winning and losing. This situation is characterised by risk. However, if the die has an unknown bias, the situation is characterised by uncertainty.

The latter applies to all situations in which one knows that there is a chance of winning and losing but has no information on the exact distribution of these chances. (line break added)

And here’s another explanation from Roser:

In a locus classicus, Luce and Raiffa (1957, p. 13) distinguish risk and uncertainty according to whether probabilities are known or completely unknown or not even meaningful.

Does the distinction make sense?

What does it mean for a probability to be “known”? What does it mean for a probability to be “completely unknown”, or “not even meaningful”? Can we find a clear, sharp way of separating all probabilities into just the two categories of (a) those we can “know” and (b) those which must remain “completely unknown”?

As far as I can tell, the answer to that last question has to be “No.” This is essentially based on the following premises:

  • P1: The answer being “Yes” would require it being the case that:

    • P1a) There are some probabilities that we can absolutely certainly know, and/or
    • P1b) There are some probabilities that we can have absolutely no knowledge about (and for which we can’t even use something like an uninformative prior).

  • P2: P1a is false, because we can never validly be (or at least never should be) absolutely certain of anything.

  • P3: P1b is false, because we essentially always have at least some, incredibly flimsy basis for coming to a probability estimate for something, or, failing that, can use some type of uninformative prior. (I’m less confident in this premise than in the previous ones, and also less sure how to phrase what I mean.)

I can’t offer a proof of these premises (note: this doesn’t mean that a proof is impossible, just that I don’t know of one). Instead, what I’ll do below is try to illustrate why I believe those premises by:

  • returning to examples that one of the authors quoted previously gave specifically for the purpose of highlighting the claimed distinction between risk and uncertainty
  • arguing that these examples do not in fact show cases in which we can absolutely certainly know some probabilities and have absolutely no knowledge about others.

I claim that, in the absence of an alternative good example that does demonstrate P1a or P1b, this provides fairly strong evidence for P2 and P3, at least.

Certain knowledge of a probability?

In some situations, we can calculate the objective probabilities of events a priori, for instance, the chances of a (fair) die showing a six. In other cases, probabilities can be estimated statistically from data, for instance, the chances of being wrongly diagnosed [with] cancer when participating in regular screenings. Both cases are referred to as situations of risk. (source)

But how do we actually know that that’s a fair die? What if someone swapped it out at the last minute? And, even if it is what we’d typically call a “fair die”, how do we know that that means the odds it’ll show a six are ⅙? What if it’s become slightly eroded - entirely accidentally - such that it has a slightly higher chance of showing a six than showing another number? What if the person throwing the die knows how to throw it such as to increase or decrease the odds it’ll land on six?

Or as Yudkowsky’s flair for the dramatic puts it:

The die might land on its edge; or get struck by a meteor; or the Dark Lords of the Matrix might reach in and write “37” on one side.

None of this stops me from happily believing that the odds are ⅙ that a die I have “very strong reason to believe” is “fair” will show a six. Nor will it stop me making bets on that basis. But it seems to me to highlight that there’s at least some doubt about what probability I should assign, and thus that this example doesn’t demonstrate P1a (i.e., doesn’t demonstrate that there are any probabilities I should be absolutely certain about).

Similar arguments could be run against the idea that the chances of being wrongly diagnosed with cancer can be absolutely, certainly known. (On top of the obvious possibilities like methodological errors in relevant studies, it’s also possible that the person’s very concept of cancer itself doesn’t line up well with reality or with the concept used by the relevant studies.)

Zero knowledge of a probability?

But might P1b be true - might there be probabilities we can have absolutely no knowledge about (and for which we can’t even use something like an uninformative prior)? I don’t believe I’ve ever encountered an example of such a probability. To return to the example given earlier:

there are situations with so many unique features that they can hardly be grouped with similar cases, such as the danger resulting from a new type of virus, or the consequences of military intervention in conflict areas. These represent cases of (Knightian) uncertainty where no data are available to estimate objective probabilities. While we may rely on our subjective estimates under such conditions, no objective basis exists by which to judge them (e.g., LeRoy & Singell, 1987). (source)

But are those situations really absolutely unique? Do we really have no (relevant) data available? What about previous viruses? What about previous military interventions? Of course situations may be very, very different in the case at hand, and that data may be of very little relevance, barely narrow things down at all, and still leave your guesses as very likely to be quite inaccurate. But isn’t it something?

To see that some data we have is at least slightly relevant, consider your reaction if I told you that the number of deaths from this new virus or new military intervention (which will occur sometime in the next 20 years) would be somewhere between 0 and 1 million, rather than somewhere between 1 trillion and 1 trillion & 1 million (i.e., more than the entire population of Earth). You’d be confident saying which of those is more likely, wouldn’t you?

And I think we’d both agree that that’s not just overconfidence - you do have legitimate reasons for your judgements there.

In fact, Tetlock’s work has empirically shown that it is possible to reliably do better than chance (and better than just “between 0 and 1 million”) in predicting events very much like those, at least over spans of a few years.[3]

As with my rejection of P1a, what I’ve said is merely suggestive of P1b’s falsity - it’s still possible that there are some probabilities we can have absolutely no knowledge of. But I’ve seen various claimed examples of situations of (Knightian) uncertainty, and none have seemed to be ones in which we can have absolutely no knowledge of the probability. (Further discussion here.) And I suspect, though here I’m quite unsure, that if there was a good example, it’d still be possible to use something like an uninformative prior to deal with it, in the absence of anything better.

Altogether, I find myself fairly confident that Premises 1-3, or statements sufficiently like them, are true, and thus that it does not make sense to speak of an absolute, binary distinction between “risk” and “uncertainty”.

But why does that matter anyway? The next section discusses some decision-making procedures that people have proposed based on the idea that there is a risk-uncertainty distinction, and why these procedures seem strange and suboptimal.

Decision-making given this distinction

Many people argue that that maximising expected utility, or even just using expected value reasoning or explicit probabilities (EP) at all, is impossible or inappropriate when facing (Knightian) uncertainty rather than risk.[4][5] As Roser writes: “According to a popular view, then, how we ought to make policy decisions depends crucially on whether we have probabilities.” Roser goes on to discuss three existing proposals for alternatives to standard usage of EPs when in situations of “uncertainty”, and why he rejects them; this is what I turn to now.

Principle of indifference

Roser:

The Principle of Indifference The first principle (also called the Principle of Insufficient Reason) suggests that if we have no probabilities, we ought to assign equal probabilities to all possible outcomes. We can then decide on the basis of these fabricated probabilities. Many of us tacitly and informally use this principle in everyday life. But it is also explicitly relied upon in the scientific literature. For example, in an article published in Science, Wigley and Raper (2001, p. 452) assume various emission scenarios to be equally likely on account of the fact that the IPCC’s third assessment report refused to make probability statements in this respect.

However, there is a widely acknowledged problem with the Principle of Indifference: there is often no natural way to individuate the consequences which one should treat as equally probable. [See Roser's paper for details.]

Maximin

Roser:

Maximin While the first strategy for decision-making without probabilities suggests making up probabilities, the second and most prominent strategy goes a different way. The Maximin Principle only characterizes consequences of policies as possible or impossible rather than as more or less probable. It proposes to rank policies by their worst possible consequence and to choose the policy with the least bad worst consequence.

The problem with Maximin lies in determining the worst possible consequence. There are various notions of possibility such as epistemic, logical, physical, or metaphysical possibility. According to any of these, the worst possible consequence of any climate policy currently on the table would seem to include the extinction of humanity or even worse catastrophes. This is hardly helpful for choosing among them.

The literature therefore suggests that we should not rely on a literal understanding of ‘‘possible’’ when espousing Maximin [cf. for example Gardiner (2006, p. 51) or Resnik (2003, pp. 336–337)]. Rather, if Maximin is to convince at all, the worst possible consequence must be understood as, say, the worst ‘‘realistic’’ consequence or the worst ‘‘plausible’’ consequence [which in turn could for example translate into us understanding the mechanism by which it could occur (cf. Shue 2010, p. 148)]. However, this brings up a problem. What does it mean for a consequence to be realistic? A consequence must count as realistic if the available evidence gives it at least some minimal support. Judging a consequence to have a certain minimal level of evidential support, however, precisely means judging it to have a certain minimal probability. Thus, realism judgements are nothing but probability judgements. ‘‘Realistic’’ is just another word for ‘‘not highly improbable’’.

This undermines the plausibility of Maximin as a decision-principle in the absence of probabilities, as it implies an availability of probabilities. If our evidence is such as to allow for a judgement about the realistic range of consequences, this same evidence surely allows for at least some probability judgements within and beyond that range. Maximin, however, suggests to arbitrarily limit our attention to the probability judgements needed for delineating the realistic range and not to make use of any probabilities within or beyond that range.

See Roser’s paper for what I see as a convincing example of the sort of problems maximin can lead to. Further discussion of why maximin, or something quite similar, seems a flawed approach can be found in this series of posts by Soares.[6]

Avoiding a lack of probabilities

Roser:

Avoiding a Lack of Probabilities A third option for choosing policies in the absence of probabilities consists in limiting the menu to those options which allow for probability assignments. [...] This line of thinking is familiar from Ellsberg (1961). Consider the following scenario:

Scenario A: You must choose between drawing a lottery ticket (i) from an urn with 50% winning tickets or (ii) from an urn with an unknown proportion of winning and losing tickets.

In this scenario many would choose from the first urn. This is hardly irrational. However, assume a modified scenario:

Scenario B: You must choose between drawing a lottery ticket (i) from an urn with 1% winning tickets or (ii) from an urn with an unknown proportion of winning and losing tickets.

In that case, it is less clear what choice would be rational. The Principle of Avoiding a Lack of Probabilities would still recommend drawing a ticket from the first urn. But we might instinctively resist this (probably on the basis of an unjustified application of the Principle of Indifference). The problem is that it seems hopeless to justify our intuitive choices in either scenario A or B. Even though we are drawn to decide in line with the Principle of Avoiding a Lack of Probabilities in some cases (such as scenario A), a reason to support this intuition is not forthcoming.

Further discussion of situations like Scenarios A and B, and of the ambiguity aversion involved, can be found in the abovementioned series of posts from Soares.

A quote from Bostrom and Ćirković may further highlight the lack of rationale for, and potential scale of harms from, following the principle of Avoiding a Lack of Probabilities:

Although more rigorous methods are to be preferred whenever they are available and applicable, it would be misplaced scientism to confine attention to those risks that are amenable to hard approaches. Such a strategy would lead to many risks being ignored, including many of the largest risks confronting humanity. It would also create a false dichotomy between two types of risks – the ‘scientific’ ones and the ‘speculative’ ones – where, in reality, there is a continuum of analytic tractability.

Do we have a choice?

As Roser notes, despite all these issues, if there was an absolute, binary risk-uncertainty distinction, it might be preferable - or necessary - to use one of these three principles rather than a standard usage of EPs. However, as discussed above, it seems that there isn’t such a distinction. Thus, we do have a choice in the matter.

So it seems that, at least in the case of an ideal agent, it would be best to use whatever probabilities we do have, even if they’re incredibly poorly grounded, as they’d still be better than nothing. Roser writes:

It is difficult to see how foregoing whatever epistemic access to the features of the options at stake we have could lead to better policy decisions than making use of it. This would be comparable to a visually impaired pilot closing her eyes on account of the impairment rather than using whatever impressions she can glean from her limited eyesight. Discarding low-credentials-probabilities amounts to wasting information. [See here for what Roser means by “low-credentials-probabilities”.]

My next post will discuss the more complicated matter of to what extent that argument applies in practice, for actual humans, given issues like the time costs involved in using EPs and tendencies towards overconfidence and anchoring.

Unknown unknowns

Here’s one last statement of the risk-uncertainty distinction (this one from Holden Karnofsky):

"Risk" refers to the probabilities seen in well-understood and robust models, [...] such that one can be confident in what would happen over a large number of trials but not over a small number. "Uncertainty" refers to fuzzy, poorly modeled lack of understanding (or to "missing pieces of one's model")[.]

This quote makes more explicit the idea that (Knightian) uncertainty could be understood as including unknown unknowns (“missing pieces of one’s model”), rather than just “unknown” probabilities for the things one is modelling (which can be considered “known unknowns”). It could also be understood as including the related idea of “black swans”.

These concepts are sometimes ignored, sometimes implicit, and sometimes explicit in discussions of a risk-uncertainty distinction. Here I’ll explain how I think they fit into the picture. This is the section of this post where I’m least confident about both how true my beliefs are and how clearly I explain those beliefs.

I think unknown unknowns that influence the likelihood of whatever proposition we’re trying to work out the probability of are a key and common reason why the probability estimate we arrive at may be quite poorly grounded, flimsy, untrustworthy, etc. I think they’re also a key and common reason why the situation may look to some like a situation of Knightian uncertainty. But this doesn’t require fundamentally different approaches to creating or interpreting of one’s probability estimates. Soares gives a useful example:

Consider the event "there is a cure for Alzheimer's disease 70 years from now".

As an aspiring Bayesian, I can assign a credence to this event. But as a denizen in a world of chaos, I can also expect black swan events. Dealing with the black swans doesn't require any new type of probability, though: I can account for it within the Bayesian framework.

Soares notes that black swans could include possibilities like “Within 70 years, human civilization will have collapsed”, but that obviously that particular example is no longer a black swan for us, as we’re now considering it. The black swans are those events we haven’t even thought of. He goes on:

I don't know where to expect black swans, but I can ask questions like "how will the average black swan affect Alzheimer's cures?". If I expect that most black swans will make Alzheimer's cures easier to achieve, then I adjust my credence upwards. If I expect the opposite, then I adjust my credence downwards.

And if I expect that I have absolutely no idea what the black swans will look like but also have no reason to believe black swans will make this event any more or less likely, then even though I won't adjust my credence further, I can still increase the variance of my distribution over my future credence for this event.

In other words, even if my current credence is 50% I can still expect that in 35 years (after encountering a black swan or two) my credence will be very different. This has the effect of making me act uncertain about my current credence, allowing me to say "my credence for this is 50%" without much confidence. So long as I can't predict the direction of the update, this is consistent Bayesian reasoning.

As a bounded Bayesian, I have all the behaviors recommended by those advocating Knightian uncertainty. I put high value on increasing my hypothesis space, and I often expect that a hypothesis will come out of left field and throw off my predictions. I'm happy to increase my error bars, and I often expect my credences to vary wildly over time. But I do all of this within a Bayesian framework, with no need for exotic "immeasurable" uncertainty.

But what if the unknown unknown doesn’t just influence what we’re trying to get a probability estimate for, but instead it is what we’re trying to get a probability estimate for? Soares discusses this too:

we are bounded reasoners, and we usually can't consider all available hypotheses. We can't expect to generate even the top ten most likely hypotheses, no matter how long we have to brainstorm. [...]

This phenomena is worrisome when attempting to predict the future, but we don't need a new kind of uncertainty to deal with the failure mode. In fact, this failure mode is nothing but a description of one of the limitations of a bounded Bayesian reasoner.

Bounded Bayesian reasoners should expect that they don't have access to the full hypothesis space. Bounded Bayesian reasoners can expect that their first-order predictions are incorrect due to a want of the right hypothesis, and thus place high credence on "something I haven't thought of", and place high value on new information or other actions that expand their hypothesis space.

That argument seems fairly sound to me. But parts of MIRI’s more recent writings on embedded agents being smaller than their world models have seemed to me to indicate that Soares' suggestions may be insufficient. But even if that’s the case, I think that's a separate problem, rather than something that reveals that there's a binary risk-uncertainty distinction. Essentially, I think it'd only show that one can't have a probability estimate for something one hasn't thought of, not that there are some propositions or evidence bases that, by their nature, fundamentally allow no probability estimates (even when one is looking at the proposition and trying to come up with an estimate).

(But again, I’m less sure of both my thinking and explanation on this, and think it’s somewhat tangential to the risk-uncertainty distinction, so I’ll leave that there.)

Closing remarks

In this post, I’ve:

  • outlined what the risk-uncertainty distinction is meant to mean
  • argued that no absolute, binary risk-uncertainty distinction exists
  • argued that imagining that there is such a distinction can lead to strange and suboptimal decision-making procedures

But, practically speaking, for humans, could there be benefits to acting as if one believes there is such a distinction? I’ll cover this question in my next post (ultimately arguing that the answer is probably “No”).

  1. Additionally, it’s sometimes unclear whether proponents of the distinction are merely arguing (a) that people perceive such a distinction, so it’s useful to think about and research it in order to understand how people are likely to think and behave, or are actually arguing (b) that people should perceive such a distinction, or that such a distinction “really exists”, “out there in the world”. It seems to me that (a) is pretty likely to be true, but wouldn’t have major consequences for how we rationally should make decisions when not certain. Thus, in this post I focus exclusively on (b). ↩︎

  2. It seems unfortunate that this distinction uses familiar words in a way that’s very different from their familiar usage. As Gooen writes, after introducing these less typical meanings of risk and uncertainty:

    Disagreeing with these definitions are common dictionaries and large parts of science and mathematics. In the Merriam-Webster dictionary, every definition of ‘risk’ is explicitly about possible negative events, not about general things with probability distributions. (https://www.merriam-webster.com/dictionary/risk)

    There is even a science explicitly called “uncertainty quantification”, but none explicitly called “risk quantification”.

    This is obviously something of a mess. Some business people get confused with mathematical quantifications of uncertainty, but other people would be confused by quantifications of socially positive “risks”.

    Roser further emphasises similar points:

    Not only in the past, but also today there is no universally accepted distinction between risk and uncertainty based on whether we have probabilities or not. This holds, of course, for everyday discourse which does not adhere to the technical distinction. But even in scientific and philosophical contexts, only some authors subscribe to the convention to use the terms risk and uncertainty in this specific way. For example, while the Intergovernmental Panel on Climate Change (IPCC) (2014, p. 155) draws a distinction between risk and uncertainty, it is completely different from the distinction at stake here. For instance, the IPCC takes probability density functions to be a common tool for characterizing uncertainty. One of the most famous microeconomics textbooks discusses decisions on the basis of probabilities under the heading of ‘‘Choice under Uncertainty’’ (Mas-Colell et al. 1995, ch. 6). More generally, there has been a long stream of economists who have dismissed the distinction and labelled it ‘‘sterile’’ or not ‘‘valid’’ (Hirshleifer and Riley 1992, p. 10; Friedman 1976, p. 282).

    ↩︎

  3. Tetlock: “The best forecasters [...] we find are able to make between 10 and 15 distinguished… between 10 and 15 degrees of uncertainty for the types of questions that IARPA is asking about in these tournaments like whether Brexit is going to occur or if Greece is going to leave the eurozone or what Russia is going to do in the Crimea, those sorts of things. Now, that’s really interesting because a lot of people when they look at those questions say, “Well you can’t make probability judgements at all about that sort of thing because they’re unique.”

    And I think that’s probably one of the most interesting results of the work over the last 10 years. I mean, you take that objection, which you hear repeatedly from extremely smart people that these events are unique and you can’t put probabilities on them, you take that objection and you say, “Okay, let’s take all the events that the smart people say are unique and let’s put them in a set and let’s call that set allegedly unique events. Now let’s see if people can make forecasts within that set of allegedly unique events and if they can, if they can make meaningful probability judgments of these allegedly unique events, maybe the allegedly unique events aren’t so unique after all, maybe there is some recurrence component.” And that is indeed the finding that when you take the set of allegedly unique events, hundreds of allegedly unique events, you find that the best forecasters make pretty well calibrated forecasts fairly reliably over time and don’t regress too much toward the mean.” ↩︎

  4. Note that one doesn’t necessarily have to accept maximising expected utility if one rejects the binary risk-uncertainty distinction. (E.g., one might choose a modification of maximisation of expected utility to avoid the issue of Pascal’s mugging.) Roser writes:

    while I believe that we always have probabilities, this paper refrains from taking a stance on how we ought to decide on the basis of these probabilities. The question whether we have probabilities is completely separate from the question how we ought to make use of them. Here, I only ask the former question. The two issues are often not kept separate: the camp that is in favour of relying on probabilities is often associated with processing them in line with expected utility theory. I myself am in favour of relying on probabilities but I reject expected utility theory (and related stances such as cost-benefit analysis), at least if it comes as a formal way of spelling out a maximizing consequentialist moral stance which does not properly incorporate rights.

    By the same token, the question of whether there’s a binary risk-uncertainty distinction is relevant even if one rejects maximisation or expected utility, as Roser also notes: “A lack of probabilities is not only a challenge for expected utility theory—which is known for its need for probabilities—but for all practical reasoning.” ↩︎

  5. For example, Andreas Mogensen writes:

    In section 2.2, I reject what I take to be a naïve but tempting response [to the problem of cluelessness]. On this view, we needn’t worry about our ignorance of the indirect effects of our actions, because ignorance of this kind is compatible with expected utility maximization. This underestimates the depth of the problem. Using the jargon proposed by Knight (1921), I suggest that we are dealing not with risk, but uncertainty: ignorance of a kind so deep that our evidence does not warrant assigning precise probabilities to all relevant contingencies. Under Knightian uncertainty, the doxastic attitudes of an agent who proportions her beliefs to the evidence cannot be represented by a unique probability function relative to which an expected utility for each act may be defined.

    Indeed, it seems to me that the whole idea of cluelessness is premised on the idea of an absolute, binary risk-uncertainty distinction, or on something that’s very much like that distinction and that suffers from the same problems as that distinction does. I therefore hope to later write a post attempting to “dissolve” the problem of cluelessness, using arguments quite similar to the above. For now, part of my thoughts on the matter can be found in two comments here, or extrapolated from what I say in this post. ↩︎

  6. In Soares’ posts, he refers to what he’s critiquing as “maximiz[ing] minimum expected utility given [one’s] Knightian uncertainty”. I believe that this is either the same as or very similar to maximin, but it’s possible I’m wrong about that. ↩︎

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[-]romeostevensit20

I found Marr's levels highly helpful when trying to think about this area. YMMV. Marr's levels also correspond to Aristotle's four causes if we do as Marr does and split the algorithmic level into 'representation' and 'traversal.'

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[-]jmh10

Here are my initial thoughts -- I may want to add or detract if I have some more time to think about this.

I think a big distinction between risk and uncertainty is perhaps more about how we manage them than really about how well we can assess the likelihood of the events. However, that plays a very large part in how to manage so becomes part of the definitions and classifications.

So, yes, I do still see these two as categorically different than merely differing in degree.

At least when I think about managing risk, not only am I assessing some outcome/payoff but also thinking of that over time -- it is an iterated setting where I can say I have reasonably good knowledge (some observation or frequencies, understanding of the process and key parameters and what values might be seen). In this type of setting think about a casino and the house rules. The house sets up the rules so they have something like a 3% edge on all the customers. They have no idea on what any given bet will pay off for them but over all the bets over the whole year, they can be pretty sure that they keep 3% if all money put down during the year.

We can step away from that very controlled setting to where we don't get to make the rules we want but still are in an iterative setting. The confidence interval for the outcome over time widens up some/a lot but the general approach can stay the same. You're going to evaluate the setting and come up with your expected outcome and make your decision.

But lets know thing about a case of a gambler. What if he can get the same edge as the house was getting? Is he really in the same situation of risk management as the casino? I think that depends. We might know what the probabilities are and the shape of the function but we don't really know how many times we need to play before our sampling starts to reflect that distribution -- statistics gives us some ideas but that also has a random element to it. The gambler's has to decide if he has a budget to make it through far enough to take advantage of the underlying probabilities -- that is to take advantage of "managing the risk".

If the gambler cannot figure that out, or knows for a fact there are insufficient funds, do those probabilities really provide useful information on what to expect? To me this is then uncertainty. The gamble simply doesn't get the opportunity to repeat and so get the expected return. In this type of situation, perhaps rather than trying to calculate all the odds, wagers and pay-offs maybe a simple rule is better if someone wants to gamble.

I think this is a situation similar to the old saying about investing in markets (particularly on the short side): the market can stay irrational a lot longer than you can stay solvent. It's also interesting here, if you have never looked into it. Traders are largely rule following animals -- not to say that they don't do a lot of analysis but that they never let their analysis lock them into a loss. I think financial markets are a great setting where one sees both risk and uncertainty.

I don't think the above is a comprehensive definition of uncertainty or risk (much more so with risk) but hopefully helps tease out at least some aspects of the difference.


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[-]MichaelA10

(As per usual, my comments are intended not to convince but to outline my thinking, and potentially have holes poked in it. I wouldn't be willing to spend time writing as many paragraphs as I do if I thought there was 0 chance I'd end up learning something new as a result!)

I don't think either the gambling or market analogies really shows either that the risk-uncertainty distinction makes sense in categorical terms, or that it's useful. I think they actually show a large collection of small, different issues, which means my explanation of why I think that may be a bit messy.

The house sets up the rules so they have something like a 3% edge on all the customers. They have no idea on what any given bet will pay off for them but over all the bets over the whole year, they can be pretty sure that they keep 3% if all money put down during the year.

I think this is true, but that "something like" and "pretty sure" are doing a lot of the work here. The house can't be absolutely certain that there's 3% edge, for a whole range of reasons - e.g., there could be card-counters at some point, the house's staff may go against their instructions in order to favour their friends or some pretty women, the house may have somehow simply calculated this wrong, or something more outlandish like Eliezer's dark lords of the Matrix. Like with my points in the post, in practice, I'd be happy making my bets as if these issues weren't issues, but they still prevent absolute certainty.

I don't think you were explicitly trying to say that the house does have absolute certainty (especially given the following paragraph), so that's sort of me attacking a straw man. But I think the typical idea of the distinction being categorical has to be premised on absolute certainty, and I think you may still sort-of be leaning on that idea in some ways, so it seems worth addressing that idea first.

But lets know thing about a case of a gambler. What if he can get the same edge as the house was getting? Is he really in the same situation of risk management as the casino? I think that depends. We might know what the probabilities are and the shape of the function but we don't really know how many times we need to play before our sampling starts to reflect that distribution -- statistics gives us some ideas but that also has a random element to it. The gambler's has to decide if he has a budget to make it through far enough to take advantage of the underlying probabilities -- that is to take advantage of "managing the risk".
If the gambler cannot figure that out, or knows for a fact there are insufficient funds, do those probabilities really provide useful information on what to expect? To me this is then uncertainty. The gamble simply doesn't get the opportunity to repeat and so get the expected return.

I think what's really going on here in your explicit comment is:

  • differences in the size of the confidence intervals; the house can indeed be more confident about their understanding of the odds. But it's not an absolute difference; they can't be sure, and the gambler can know something.
    • So I think it's sort-of true to say "We might know what the probabilities are and the shape of the function but we don't really know how many times we need to play before our sampling starts to reflect that distribution -- statistics gives us some ideas but that also has a random element to it." But here the "don't really know", "some ideas", and "a random element" seem to me to be doing a lot of the work - this isn't absolutely different from the house's situation; in both cases, there can be a prior, there's some data, and there's some randomness and uncertainty. The house has a way better grounded prior, way more data, and way less uncertainty, but it's not a categorical difference, as far as I can see.
  • an extreme case of diminishing returns to money. Becoming totally broke is really bad, and once you get there you can't get back. So even if he does have really good reason to believe gambling has positive expected value in dollars, that doesn't mean it has positive expected utility. I think it's very common to conflate the two, and that this is what underlies a lot of faulty ideas (i.e., that we should be genuinely risk-averse, in terms of utility - it makes a lot of sense to avoid the colloquial sense of risk, and it makes sense to avoid many gambles with positive expected dollar value, but that all makes sense if we're risk-neutral in terms of utility).

So it's very easy to reach the reasonable-seeming conclusion that gambling is unwise even if there's positive expected value in dollar terms, without leaning on the idea of a risk-uncertainty distinction (to be honest, even in terms of degrees - we don't even need to talk about the sizes of the confidence intervals, in this case).

I also think there's perhaps two more things implicitly going on in that analogy, which aren't key points but might slightly nudge one's intuitions:

  • We have a great deal of data, and very strong theoretical reasons, pointing towards the idea that, in reality, gambling has negative expected value in dollar terms. This could mean that, if Framing A seems to suggest one shouldn't gamble, and Framing B suggests one should, Framing A scores points with our intuitions. And this could occur even if we stipulate that there's positive expected value, because system 1 may not get that memo. (But this is a very small point, and I do think it's acceptable to use analogies that break our intuitions a bit, I just think it should be acknowledged.)
  • We also probably have a strong prior that gamblers are very often overconfident. It seems likely to me that, if you have a bias towards overconfidence, then the less grounding you have for your probabilities, the more likely they are to be wrong. That is, it's not just that the value you happen to receive could be further from what you expect, in either direction (compared to if you had a better-grounded probability), but that your perceived expected value is probably off the reasonable expected value by more, because your beliefs had more "room to manoeuvre" and were biased to manoeuvre i none direction in particular. So the less trustworthy our probability, the more likely it is we shouldn't gamble, as long as we're biased towards overconfidence, but we can discuss this in terms of degrees rather than a categorical distinction.
In this type of situation, perhaps rather than trying to calculate all the odds, wagers and pay-offs maybe a simple rule is better if someone wants to gamble.

I think that's likely true, but I think that's largely because of a mixture of the difficulty of computing the odds for humans (it's just time consuming and we're likely to make mistakes), the likelihood that the gambler will be overconfident so he should probably instead adopt a blanket heuristic to protect him from himself, and the fact that being broke is way worse than being rich is good. (Also, in realistic settings, because the odds are bad anyway - they pretty much have to be, for the casino to keep the lights on - so there's no point calculating; we already know which side of the decision-relevant threshold the answer must be on.) I don't think there's any need to invoke the risk-uncertainty distinction.

And finally, regarding the ideas of iterating and repeating - I think that's really important, in the sense that it gives us a lot more, very relevant data, and shifts our estimates towards the truth and reduces their uncertainty. But I think on a fundamental level, it's just evidence, like any other evidence. Roughly speaking, we always start with a prior, and then update it as we see evidence. So I don't think there's an absolute difference between "having an initial guess about the odds and then updating based on 100 rounds of gambling" and "having an initial guess about the odds and then updating based on realising that the casino has paid for this massive building, all these staff, etc., and seem unlikely to make enough money for that from drinks and food alone". (Consider also that you're never iterating or repeating exactly the same situation.)

Most of what I've said here leaves open the possibility that the risk-uncertainty distinction - perhaps even imagined as categorical - is a useful concept in practice (though I tentatively argue against that here). But it seems to me that I still haven't encountered an argument that it actually makes sense as a categorical division.

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[-]jmh10

Micheal, do so research on the way casinos work. The casino owners don't gamble on their income. Here is a link to consider: https://www.quora.com/How-do-casinos-ultimately-make-money

My point about iterations is not about getting better estimates for the probabilities. The probabilities are known, defined quantities, in the argument. The difference is that in some setting one will have the luxury of iterating and so able to actually average the results towards that expect value. If you can iterate an infinite number of times your results converge to that expected value.

Seem one implication of your position is that people should be indifferent to the following two settings where the expected payoff is the same:

1) They toss a fair coin as many times as they want. If they get heads, they will receive $60, if they get tails they pay $50.

2) They can have the same coin, and same payoffs but only get one toss.

Do you think most peoples decision will be the same? If not, how do you explain the difference.

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[-]MichaelA30
The casino owners don't gamble on their income.

Maybe this is a matter of different definitions/connotations of "gamble". Given that the odds are in the casino's favour, and that they can repeat/iterate the games a huge number of times, the results do indeed tend to converge to the expected value, which is in the casino's favour - I'm in total agreement there. The odds that they'd lose out, given those facts, are infinitesimal and negligible for pretty much all practical purposes. But it's like they asymptotically approach zero, not that they literally are zero.

It seems very similar to the case of entropy:

The Second Law of Thermodynamics is statistical in nature, and therefore its reliability arises from the huge number of particles present in macroscopic systems. It is not impossible, in principle, for all 6 × 1023 atoms in a mole of a gas to spontaneously migrate to one half of a container; it is only fantastically unlikely—so unlikely that no macroscopic violation of the Second Law has ever been observed.

But in any case, it seems your key point there, which I actually agree with, is that the deal is better for the casino (partly) because they get to play the odds more often than an individual gambler does, so the value they actually get is more likely to be close to the expected value than the individual gambler's is. But I think the reason this is better is because of the diminishing marginal utility of money - losing all your money is way worse than doubling it is good - and not because of the risk-uncertainty distinction itself.

(Though there could be relevant interplays between the magnitude of one's uncertainty and the odds one ends up in a really bad position, which might make one more reluctant to avoid "bets" of any kind when the uncertainty is greater. But again, it's helpful to consider whether you're thinking about expected utility or expected value of some other unit, and it also seems unnecessary to use a categorical risk-uncertainty distinction.)

Seem one implication of your position is that people should be indifferent to the following two settings where the expected payoff is the same:
1) They toss a fair coin as many times as they want. If they get heads, they will receive $60, if they get tails they pay $50.
2) They can have the same coin, and same payoffs but only get one toss.
Do you think most peoples decision will be the same? If not, how do you explain the difference.

Regarding whether I think people's decisions will be the same, I think it's useful to make clear the distinction between descriptive and normative claims. As I say in footnote 1:

Additionally, it’s sometimes unclear whether proponents of the distinction are merely arguing (a) that people perceive such a distinction, so it’s useful to think about and research it in order to understand how people are likely to think and behave, or are actually arguing (b) that people should perceive such a distinction, or that such a distinction “really exists”, “out there in the world”. It seems to me that (a) is pretty likely to be true, but wouldn’t have major consequences for how we rationally should make decisions when not certain. Thus, in this post I focus exclusively on (b).

So my position doesn't really directly imply anything about what people will decide. It's totally possible for the risk-uncertainty distinction to not "actually make sense" and yet still be something that economists, psychologists, etc. should be aware of as something people believe in or act as if they believe in. (Like how it's useful to study biases or folk biology or whatever, to predict behaviours, without having to imagine that the biases or folk biology actually reflect reality perfectly.) But I'd argue that such researchers should make it clear when they're discussing what people do vs when they're discussing what they should do, or what's rational, or whatever.

(If your claims have a lot to do with what people actually think like, rather than normative claims, then we may be more in agreement than it appears.)

But as for what people should do in that situation, I think my position doesn't imply people should be indifferent to that, because getting diminishing marginal utility from money doesn't conflict with reality.

In the extreme version of that situation, if someone starts with $150 as their entire set of assets, and takes bet 2, then there's a 50% chance they'll lose a third of everything they own. That's really bad for them. The 50% chance they win $60 could plausibly not make up for that.

If the same person takes bet 1, the odds that they end up worse off go down, because, as you say, the actual results will tend to converge towards the (positive in dollar terms) expected value as one gets more trials/repetitions.

So it seems to me that it's reasonable to see bet 1 as better than bet 2 (depending on an individual's utility function for money and how much money they currently have), but that this doesn't require imagining a categorical risk-uncertainty distinction.

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[-]joracine10

For the most part, you seem to spend a lot of time trying to discover whether terms like unknown probability and known probability make sense. Yet, those are language artifacts which, like everything language, is merely a use of a clarification algorithm as means to communicate abstractions. Each class represents primarily its dominating modes, but becomes increasingly useless at the margins. As such, you yourself make a false dichotomy by trying to discuss whether these terms are useful or not by showing that at the border they might fail: they fail, and they're both useful and not useful at the border, depending if the exact threshold. In fact, you even start by discussing whether the border can be objectively defined: the answer is obviously no, since it is language, and then you try to use other words to make the point, where you then do your analysis a second time on the new words, and discuss whether the classification systems for those words are perfect (i.e. zero, plausible, realistic, etc.). I think that in reality you are missing the point entirely.

These quotes and definitions are using imagery to teach readers the basic classification system (i.e. the words) to the reader, by proposing initial but vague boundaries. Then, based on the field and experience, the reader further refines this classification to further match the group's (i.e. The experts) definition. Reviews of a given set of risks and uncertainties are then about discussing a) whether the different experts are calibrated in terms of classification threshold; and b) if they feel they sufficiently are calibrated, whether the probabilities and impacts have been properly and sufficiently assessed or not (here to, these vague words are based on a given groups standards).

For example, in software engineering, plans generally include a risks section, where is described various unknowns, their probability, and their impact. Each of those are quantified by (for example) High, Medium, Low, or Unknown. This is simply a double-layer of subjective but group-agreed upon classification of words, meant to communicate the overall probability that the project will hit the date at the expected cost. It is based on experience (i.e. the internal model of the author). During the review process, other leaders and engineers then comment based on their experience on whether a specified risk is properly assessed. These threshold can be very context specific (i.e. a team, a company, or the industry). This is no different in public policy (i.e. risks and impact of global warming).

In other words, I think that you are trying to analyze the problem objectively by making each assertion absolute (i.e. a probability is known or unknown, etc.), while in fact the problem is one of pure communication, rather than one of objective truth or logic. So you get caught in a rabbit hole as you are essentially re-discovering the limitations of language and classification systems, rather than actually discussing the problem at hand. And the initial problem statement, in your analysis (i.e. certainty as risk+uncertainties) is arbitrary, and your logic could have been applied to any definition or concept.

Whether the idea of uncertainty+risk is the proper tool can essentially only analyzed empirically, by comparing it, for example, to another method used in a given field, and evaluating whether method A or B improve s the ability of planners to predict date/cost prediction (in software engineering, for example).

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[-]joracine10

In other words, I think it's more useful to think of those definitions as an algorithm (perhaps ML): certainty ~ f(risk, uncertainty); and the definitions provided of the driving factors as initial values. The users can then refine their threshold to improve the model's prediction capability over time, but also as a function of the class of problems (i.e. climate vs software).

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[-]MichaelA10

I think I agree with substantial parts of both the spirit and specifics of what you say. And your comments have definitely furthered my thinking, and it's quite possible I'd now write this quite differently, were I to do it again. But I also think you're perhaps underestimating the extent to which risk vs uncertainty very often is treated as an absolute dichotomy, with substantial consequences. I'll now attempt to lay out my thinking in response to your comments, but I should note that my goal isn't really to convince you of "my side", and I'd consider it a win to be convinced of why my thinking is wrong (because then I've learned something, and because that which can be destroyed by the truth should be, and all that).

For the most part, you seem to spend a lot of time trying to discover whether terms like unknown probability and known probability make sense. Yet, those are language artifacts which, like everything language, is merely a use of a clarification algorithm as means to communicate abstractions. Each class represents primarily its dominating modes, but becomes increasingly useless at the margins.

From memory, I think I agreed with basically everything in Eliezer's sequence A Human's Guide to Words. One core point from that seems to closely match what you're saying:

The initial clue only has to lead the user to the similarity cluster—the group of things that have many characteristics in common.  After that, the initial clue has served its purpose, and I can go on to convey the new information "humans are currently mortal", or whatever else I want to say about us featherless bipeds.
A dictionary is best thought of, not as a book of Aristotelian class definitions, but a book of hints for matching verbal labels to similarity clusters, or matching labels to properties that are useful in distinguishing similarity clusters.

And it's useful to have words to point to clusters in thingspace, because it'd be far too hard to try to describe, for example, a car on the level of fundamental physics. So instead we use labels and abstractions, and accept there'll be some fuzzy boundaries and edge cases (e.g., some things that are sort of like cars and sort of like trucks).

One difference worth noting between that example and the labels "risk" and "uncertainty" is that risk and uncertainty are like two different "ends" or "directions" of a single dimension in thingspace. (At least, I'd argue they are, and it's possible that that has to be based on a Bayesian interpretation of probability.) So here it seems to me it'd actually be very easy to dispense with having two different labels. Instead, we can just have one for the dimension as a whole (e.g., "trustworthy", "well-grounded", "resilient"; see here), and then use that in combination with "more", "less", "extremely", "hardly at all", etc., and we're done.

We can then very clearly communicate the part that's real (that reflects the territory) from when we tried to talk about "risk" and "uncertainty", without confusing ourselves into thinking that there's some sharp line somewhere, or that it's obvious a different strategy would be needed in "one case" than in "the other". This is in contrast to the situation with cars, where it'd be much less useful to say "more car-y" or "less car-y" - do we mean along the size dimension, as compared to trucks? On the size dimension, as compared to mice? On the "usefulness for travelling in" dimension? On the "man made vs natural" dimension? It seems to me that it's the high dimensionality of thingspace that means labels for clusters are especially useful and hard to dispense with - when we're talking about two "regions" or whatever of a single dimension, the usefulness of separate labels is less clear.

That said, there are clearly loads of examples of using two labels for different points along a single dimension. E.g., short and tall, heavy and light. This is an obvious and substantial counterpoint to what I've said above.

But it also brings me to really my more central point, which is that people who claim real implications from a risk-uncertainty distinction typically don't ever talk about "more risk-ish" or "more Knightian" situations, but rather just situations of "risk" or of "uncertainty". (One exception is here.) And they make that especially clear when they say things like that we "completely know" or "completely cannot know" the probabilities, or we have "zero" knowledge, or things like that. In contrast, with height, it's often useful to say "short" or "tall", and assume a shared reference frame that makes it clear roughly what we mean by that (e.g., it's different for buildings than for people), but we also very often say things like "more" or "less" tall, "shorter", etc., and we never say "This person has zero height" or "This building is completely tall", or the like, except perhaps to be purposefully silly.

So while I agree that words typically point to somewhat messy clusters in thingspace, I think there are a huge number of people who don't realise (or agree with) that, and who seem to truly believe there's a clear, sharp distinction between risk and uncertainty, and who draw substantial implications from that (e.g., that we need to use methods other than expected value reasoning, as discussed in this post, or that we should entirely ignore possibilities we can't "have" probabilities about, an idea which the quote from Bostrom & Cirkovic points out the huge potential dangers of).

So one part of what you say that I think I do disagree with, if I'm interpreting you correctly, is "These quotes and definitions are using imagery to teach readers the basic classification system (i.e. the words) to the reader, by proposing initial but vague boundaries." I really don't think most writers who endorse the risk-uncertainty distinction think that that's what they're doing; I think they think they're really pointing to two cleanly separable concepts. (And this seems reflected in their recommendations - they don't typically refer to things like gradually shifting our emphasis from expected value reasoning to alternative approaches, but rather using one approach when we "have" probabilities and another when we "don't have probabilities", for example.)

And a related point is that, even though words typically point to somewhat messy clusters in thingspace, some words can be quite misleading and do a poor job of marking out meaningful clusters. This is another point Eliezer makes:

Any way you look at it, drawing a boundary in thingspace is not a neutral act.  Maybe a more cleanly designed, more purely Bayesian AI could ponder an arbitrary class and not be influenced by it.  But you, a human, do not have that option.  Categories are not static things in the context of a human brain; as soon as you actually think of them, they exert force on your mind.  One more reason not to believe you can define a word any way you like.

A related way of framing this is that you could see the term "Knightian uncertainty" as sneaking in connotations that this is a situation where we have to do something other than regular expected value reasoning, or where using any explicit probabilities would be foolish and wrong. So ultimately I'm sort-of arguing that we should taboo the terms "risk" (used in this sense) and "Knightian uncertainty", and just speak in terms of how uncertain/resilient/trustworthy/whatever a given uncertainty is (or how wide the confidence intervals or error bars are, or whatever).

But what I've said could be seen as just indicating that the problem is that advocates of the risk-uncertainty distinction need to read the sequences - this is just one example of a broader problem, which has already been covered there. This seems similar to what you're saying with:

So you get caught in a rabbit hole as you are essentially re-discovering the limitations of language and classification systems, rather than actually discussing the problem at hand. And the initial problem statement, in your analysis (i.e. certainty as risk+uncertainties) is arbitrary, and your logic could have been applied to any definition or concept.

I think there's something to this, but I still see the risk-uncertainty distinction proposed in absolute terms, even on LessWrong and the EA Forum, so it seemed worth discussing it specifically. (Plus possibly the fact that this is a one-dimensional situation, so it seems less useful to have totally separate labels than it is in many other cases like with cars, trucks, tigers, etc.)

But perhaps even if it is worth discussing that specifically, I should've more clearly situated it in the terms established by that sequence - using some of those terms, perhaps changing my framing, adding some links. I think there's something to this as well, and I'd probably do that if I was to rewrite this.

And something I do find troubling is the possibility that the way I've discussed these problems leans problematically on terms like "absolute, binary distinction", which should really be tabooed and replaced by something more substantive. I think that the term "absolute, binary distinction" is sufficiently meaningful to be ok to be used here, but it's possible that it's just far, far more meaningful than the term "Knightian uncertainty", rather than "absolutely" more meaningful. As you can probably tell, this particular point is one I'm still a bit confused about, and will have to think about more.

And the last point I'll make relates to this:

Whether the idea of uncertainty+risk is the proper tool can essentially only analyzed empirically, by comparing it, for example, to another method used in a given field, and evaluating whether method A or B improve s the ability of planners to predict date/cost prediction (in software engineering, for example).

This is basically what my next post will do. It focuses on whether, in practice, the concept of a risk-uncertainty distinction is useful, whether or not it "truly reflects reality" or whatever. So I think that post, at least, will avoid the issues you perceive (at least partially correctly, in my view) in this one.

I'd be interested in your thoughts on these somewhat rambly thoughts of mine.

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[-]MichaelA10

Update: I've now posted that "next post" I was referring to (which gets into whether the risk-uncertainty distinction is a useful concept, in practice).

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