Notes from Teigen & Brun:
The recurrent findings in these studies are (1) a reasonable degree of between-group consistency, combined with (2) a high degree of within-group variability. In other words, mean estimates of “very probable”, “doubtful” and “improbable” are reasonably similar from study to study, supporting the claim that probability words are translatable; but, at the same time, the interindividual variability of estimates is large enough to represent a potential communication problem. If, for instance, the doctor tells the patient that a cure is “possible”, she may mean a 5 per cent chance, but it may be interpreted to mean a 70 per cent chance, or vice versa. This variability is typically underestimated by the participants themselves. Brun and Teigen (1988) asked medical doctors to specify a range within which would fall 90 per cent of other doctors’ interpretations. This interval included on the average (for 14 verbal phrases) less than 65 per cent of the actual individual estimates. Amer, Hackenbrack and Nelson (1994) found that auditors’ 90 per cent ranges included, on average, only 56 per cent of the individual estimates (for 23 phrases). In other words, the problem posed by interindividual variability appears to be aggravated by a low degree of variability awareness.
...several attempts have been made to construct standard lists of verbal expressions, where each phrase is coordinated with an appropriate numeric probability (Beyth-Marom, 1982; Hamm, 1991; Tavana, Kennedy & Mohebbi, 1997; Renooij & Witteman, 1999)
...Verbal phrases are, furthermore, parts of ordinary language, and thus sensitive to conversational implicatures. So I may say that a particular outcome is somewhat uncertain, not because I think it has a low probability of occurring, but because I want to modify some actual, imagined or implied belief in its occurrence. Such modifications can go in two directions, either upwards or downwards on the probability scale. Verbal probability expressions can accordingly be categorised as having a positive or a negative directionality. They determine whether attention should be directed to the attainment or the non-attainment of the target outcome, and, in doing so, they have the ability to influence people’s judg- ments and decisions in an unambiguous way. Words may be denotatively vague, but they are argumentatively precise. If you tell me that success is “possible”, I know I am being encouraged, even if I do not know whether you have a probability of 30 per cent or of 70 per cent in mind. If you say it is “not certain”, I know I am advised to be careful and to think twice. But if you tell me there is a 45 per cent probability I will not know what to think. The information is precise, but its pragmatic meaning is undecided. Do you mean uncertainty (I have only a 45 per cent chance) or possibility (at least I have a 45 per cent chance)? Likelihood or doubt? Or both?
"Do not walk to the truth, but dance. On each and every step of that dance your foot comes down in exactly the right spot. Each piece of evidence shifts your beliefs by exactly the right amount, neither more nor less. What is exactly the right amount? To calculate this you must study probability theory. Even if you cannot do the math, knowing that the math exists tells you that the dance step is precise and has no room in it for your whims." -- from "Twelve Virtues of Rationality", by Eliezer Yudkowsky
One of the more useful mental tools I've found is the language Lojban ( http://www.lojban.org/tiki/Learning ), which makes explicit many of the implicit assumptions in languages. (There's also a sub-language based on Lojban, called Cniglic ( http://www.datapacrat.com/cniglic/ ), which can be added to most existing languages to offer some additional functionality.)
One of the things Lojban (and Cniglic) has are 'evidentials', words which can be used to tag other words and sentences to explain how the speaker knows them: "ja'o", meaning "I conclude", "za'a" meaning "I observe", "pe'i" meaning "It's my opinion", and more. However, there hasn't been any easy and explicit way to use this system to express Bayesian reasoning...
... until today.
Lojban not only allows for, but encourages, "experimental" words of certain sorts; and using that system, I have now created the word "bei'e" (pronounced BAY-heh), which allows a speaker to tag a word or sentence with how confident they are, in the Bayesian sense, of its truth. Taking an idea from the foundational text by E.T. Jaynes, "bei'e" is measured in decibels of logarithmic probability. This sounds complicated, but in many cases, is actually much easier to use than simple odds or probability; adding 10 decibels multiplies the odds by a factor of 10.
The current reftext for "bei'e" is at http://www.lojban.org/tiki/bei%27e , which basically amounts to adding Lojbannic digits to the front of the word:
By having this explicit mental tool, even if I don't use it aloud, I'm finding it much easier to remember to gauge how confident I am in any given proposition. If anyone else finds use in this idea, so much the better; and if anyone can come up with an even better mental tool after seeing this one, that would be better still.
.uo .ua .uisai .oinairo'e