Abstract
Possibility theory is applied to assessing the relative risk associated with very rare, high-consequence hazards. The probability of rare negative events has to be estimated from a few past occurrences that are spread over long exposure periods, with counter- measures added in response to each event to attempt to guard against recurrence. Traditional risk assessments based on conditional probability and statistical expected value are very sensitive to the uncertainty associated with rare events. A new measure of possibility for events whose probability is not well measurably different from zero is proposed and illustrated in the context of possible release of hazardous material from a high containment research laboratory and in the context of large insurance company failures. Strategies for managing and reducing risk that do not depend on well-measured probabilities are discussed.