The standard mathematical treatment
of risk combines numerical measures of uncertainty (usually probabilistic) and
loss (money and other natural estimators of utility). There are significant
practical and theoretical problems with this interpretation. A particular
concern is that the estimation of quantitative parameters is frequently
problematic, particularly when dealing with one-off events such as political,
economic or environmental disasters. Practical decision-making under risk,
therefore, frequently requires extensions to the standard treatment.
An intuitive approach to reasoning
under uncertainty has recently become established in computer science and
cognitive science in which general theories (formalised in a
non-classical first-order logic) are applied to descriptions of specific
situations in order to construct arguments for and/or against claims
about possible events. Collections of arguments can be aggregated to
characterize the type or degree of risk, using the logical
grounds of the arguments to explain, and assess the credibility of, the
supporting evidence for competing claims. Discussions about whether a complex
piece of equipment or software could fail, the possible consequences of such
failure and their mitigation, for example, can be based on the balance
and relative credibility of all the arguments. This approach has been shown to
offer versatile risk management tools in a number of domains, including
clinical medicine and toxicology (e.g. www.infermed.com; www.lhasa.com).
Argumentation frameworks are also being used to support open discussion and
debates about important issues (e.g. see debate on environmental risks at www.debategraph.org).
Despite the practical success of argument-based
methods for risk assessment and other kinds of decision making they typically
ignore measurement of uncertainty even if some quantitative data are available,
or combine logical inference with quantitative uncertainty calculations in ad
hoc ways. After a brief introduction to the argumentation approach I will
demonstrate medical risk management applications of both kinds and invite
suggestions for solutions which are mathematically more satisfactory.
Definitions (Hubbard: http://en.wikipedia.org/wiki/Risk)
Uncertainty:
The lack of complete certainty, that is, the existence of more than one
possibility. The "true" outcome/state/result/value is not known.
Measurement of uncertainty: A
set of probabilities assigned to a set of possibilities. Example:"There is
a 60% chance this market will double in five years"
Risk: A
state of uncertainty where some of the possibilities involve a loss,
catastrophe, or other undesirable outcome.
Measurement of risk: A
set of possibilities each with quantified probabilities and quantified losses.
Example: "There is a 40% chance the proposed oil well will be dry with a
loss of $12 million in exploratory drilling costs".
The conceptual background to the
argumentation approach to reasoning under uncertainty is reviewed in the
attached paper “Arguing about the Evidence: a logical approach”.