What Does “Likely” Mean? (Estimative Probability)

I typically take some time out on Saturday mornings to do some reading. This often begins with developments in personal finance or computer science, though there’s a tendency to branch out from that; I generally don’t restrict myself from going off on tangents.

For some reason, this week I came across a Masters thesis discussing communication of probabilities, specifically in the intelligence domain. It seems that I found it via A Wealth of Common Sense, a blog concerning personal finance that I read occasionally; there was a link there to a Library of Economics blogpost discussing issues with mapping qualitative descriptions to quantitative probabilities. For example, if I say that something is highly likely to happen, I would be implying that I believe it would happen with probability at least N; however, the numerical value of N is uncertain, and differs among different people.

For me at least, N would be around 80 percent (and, incidentally, the author of that post agrees); that said, I can certainly envisage people assigning values of N as low as 0.6 or as high as 0.95. Note that the problem can also be two-tailed (e.g. about evenmightpossiblenot inconceivable). The LoE author’s son proposes a reasonable scheme, which is to have authors outline their own mapping in a glossary. This is probably (well, I mean P >=0.7) a good first step, though there are implementation challenges in terms of length as well as completeness.

It turns out that the concept of words of estimative probability is treated very seriously in the intelligence domain. It is understandably important, as briefs are typically prepared in natural language, and often need to be communicated to audiences that may not be entirely comfortable with mathematical notation. To quote a CIA officer:

Most consumers of intelligence aren’t particularly sophisticated when it comes to probabilistic analysis. They like words and pictures, too. My experience is that [they] prefer briefings that don’t center on numerical calculation. That’s not to say we can’t do it, but there’s really not that much demand for it.

Furthermore, deriving highly precise (though possibly not highly accurate) estimates for probabilities is almost certainly (*cough* I mean P <= 0.03) pointless, and is likely (P >= 0.7) damaging in that it tends to (P >= 0.6) give a false sense of security and accuracy when that does not actually exist.

The original proposal divides probabilities onto a seven-point scale (arguably five, as the ends are meant to reflect absolute certainties): certain, almost certain, probable, chances about even, probably not, almost certainly not, impossible. I think most people would agree that the above ordering is in decreasing order of probabilities. Of course, strictly adhering to the above labels would impart a degree of awkwardness to writing, and a group of variants for each level (such as highly doubtful for almost certainly not) soon developed.

Interestingly, the author also gives possible a fairly specific meaning; he defines it to mean “greater than zero and less than one” (which makes sense; of course, something always happening is certainly possible – but it seems pointless to not use the more precise word), but also adds the restriction that “no numerical odds (can) be assigned”. This seems like a useful construct, especially in the early stages of knowing things when uncertainty tends to be high; the other descriptive terms were conceived with uncertainty ranges of about 10% on each side.

The author of the Masters thesis also considers how words of estimative probability are used in other fields. I found the comparison to weather forecasting particularly interesting, as the author rightly points out that that is one field in which the general public is given numeric estimates (of the probability of precipitation). Weather forecasters typically add their own prose when reporting as well, which allowed some comparison. That said, a major difference is that in forecasting, these estimates can be derived with fair precision (and, as it turns out, accuracy) as they can (and, in the UK, do) originate from predictive models of atmospheric conditions. There seem to be standardised terms as far as the US National Weather Service is concerned, though I wasn’t able to find comparable guidance from the UK Met Office.

The clarity required from words of estimative probability depends on the consequences of miscommunication, as well. This is of course important in intelligence, with some claiming that there was miscommunication regarding warnings related to the September 11 terrorist attacks. Incorrectly reporting a weather forecast is almost certainly (ugh, P >= 0.95) less consequential, though people may make bad decisions concerning taking umbrellas when going out or hanging clothes out to dry. I can imagine contexts where this would also be very important (such as experimental trials in medicine or financial planning), though it seems for the most part some degree of ambiguity or even unknown disagreement is probably okay.

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