Tuesday 10 December 2013

Language barriers in understanding risk and uncertainty

Arthur Charpentier and Dave Giles  reminded me of the disagreement over the terms random and chance variable.
and brought to my mind the misunderstandings that can occur when economists use the word "risk".  Following Frank Knight, economists will often use the word "risk" to represent a 'known probability', where as an "uncertainty" is an 'unkown' probability.  Knight gives a business example:
the bursting of bottles does not introduce an uncertainty or hazard into the business of producing champagne; since in the operations of any producer a practically constant and known proportion of the bottles burst, it does not especially matter even whether the proportion is large or small. The loss becomes a fixed cost in the industry and is passed on to the consumer, like the outlays for labour or materials or any other.
I have never found Knight's distinction particularly helpful because  the word "risk" is commonly used to represent the possibility of a loss:
 OED 1. (Exposure to) the possibility of loss, injury, or other adverse or unwelcome circumstance; a chance or situation involving such a possibility. 
with the first example appearing in 1621.  The word originates in post-classical Latin, either from the classical Latin  resecare, "something that cuts" i.e. rocks, or from the Arabic rizq which has a number of meanings: ‘provision, lot, portion allotted by God to each man’, ‘livelihood, sustenance’, hence ‘boon, blessing (given by God)’, ‘property, wealth’, ‘income, wages’, and finally ‘fortune, luck, destiny, chance’.

I prefer to use "chance" in place of Knight's "risk"
OED 1 The falling out or happening of events; the way in which things fall out; fortune; case.
from the Latin cadere, 'to fall', highlighting the relationship between "chance" and the roll of the dice.  The association between "chance" and probability was established by de Moivre with his Doctrine of Chances.  While it is unwise to contradict the Oxford English Dictionary (OED) I tend to think chance is derived from the Dutch word kans.

Ian Hacking discusses the problems Huygens, who like all Dutch mathematicians of the time wrote firstly in Dutch and then translated into Latin for an international audience, had in translating the work kans, which according to Google translate can mean either 'chance' or 'opportunity'.  The obvious Latin equivalent for kans as chance would have been sors, 'lot'. Huygens, or possibly his editor Schootens, chose expectatio, highlighting the association between chance and opportunity, where as Knight had associated it with risk.  An alternative to expectatio that Huygens considered was spes, which was the Latin word for the Christian virtue 'Hope' and is related to a Roman goddess for hope.  The French still employ the word esperance for mathematical expectation while the English use expectation (the Dutch use verwachting which has a number of translations (depending on the context): 'hope, promise, expectation, forecast, prognosis').

Knight did not really innovate his use of "risk", according to the OED it originates with de Morgan
OED2b. The error of an observation or result considered without regard to sign; the probability of an error; the mean weighted loss incurred by a decision taken or estimate made in the face of uncertainty; spec. = mean-square error 
De Morgan defined it in 1832
 This is what Laplace calls l'erreur moyenne √† craindre en plus, and the corresponding error en moins is of the same magnitude with a different sign. We shall call it the risk of the observation, the sign of the error not being considered.
 My interpretation is that De Morgan's thinking is closely related to Quetelet's - a deviation from the norm is a risk - see my previous post on this.

The word "random" seems very inappropriate, apparently originating in Middle French randon, meaning 'speed' or 'hast'.  We have
OED A1a. Impetuosity, great speed, force, or violence (in riding, running, striking, etc.); chiefly in with (also in) great random .  (earliest occurrence 1325)
OED A2a. Gunnery. The range of a piece of ordnance, esp. the long or full range obtained by elevating the muzzle of the piece.  (earliest occurrence 1560)
OED A 3. A haphazard or aimless course.  (earliest occurrence 1565)
and the first use as an adverb and adjective
OED B1 At random, randomly. (earliest occurrence 1619)
OED C1a. Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard.  (earliest occurrence 1655)
The first use in mathematics was in 1884:
Applying the Calculus of Probabilities..to the question of whether the distribution of the fixed stars can be regarded as the result of a random sprinkling.
A mathematician might use stochastic as an adjective in preference to random or chance.  The word derives from the Greek 'to aim at a mark, guess' according to the OED, my Greek PhD supervisor said it related to shooting arrows.  Its first appearance in English was in 1662
But yet there wanted not some beams of light to guide men in the exercise of their Stocastick faculty.
and then in 1688 in Cudworths Treatise on Free Will
There is need and use of this stochastical judging and opining concerning truth and falsehood in human life.
What do I conclude:  there is no certainty in what we are talking about when using words like risk, chance, random etc. and it is not surprising we have difficulty dealing with the concept.

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