
06458036
j
2015e.00837
Borovcnik, Manfred
Risk and decision making: the ``logic" of probability.
Math. Enthus. 12, No. 13, 113139 (2015).
2015
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
K70
K90
M40
risk
definition
hazard
uncertainty
economic theory
utility
risk management
statistical inference
hypothesis testing
risk perception
decision making
statistical errors
risk with low probabilities
psychological aspects
Bayesian risk
minimax principle
repeated decisions
insurances
medicine
odds
stakeholders
societal risks
Zbl 1225.91017
http://www.math.umt.edu/tmme/vol12no1thru3/12_Borovcnik.pdf
Summary: Risk is a hot topic. There is an international trend to use examples of risk or the concept of risk in the early teaching of probability. It enriches the problems, it widens the contexts, and it motivates the students to learn probability. This paper illustrates the notion of risk as a multifaceted concept. The diverse perceptions start with language where risk is used in very different ways. The overlap of risk and hazard is not restricted to the technical context of safety and reliability; {\it F. H. Knight}'s seminal work on risk and uncertainty [Risk, uncertainty, and profit. Boston, MA: Hart, Schaffner \& Marx; Houghton Mifflin Company (1921)] has its definite impact on today's perception of the notions. The endeavour to reinterpret issues of statistical inference by risk  the risk of type I and II errors  or the concept of the weighted impact of decisions (in decision theory and in Bayesian framework) can clarify what risk means within mathematics but  as the whole machinery of statistical inference is difficult to understand  it may have little consequence on how the majority of people act and understand the notion of risk. {\it A. Tversky} and {\it D. Kahneman} [Science 211, No. 4481, 453458 (1981; Zbl 1225.91017)] show that the perception of risk is influenced by psychological factors and assert that people are risk averse in winning situations while they are risk seeking in losing situations. The perception of risk is dominated by the impact (loss or win) so that even a thorough judgement of the underlying probabilities is biased. If risk is shared between several stakeholders, they all have to use their own ingredients for their model of the same situation and follow their own logic. This leads to nonunique answers, which is unusual in mathematics. Methods of simplifying problems, the way to find a solution, and understand the underlying concepts more easily may induce a shift from a refined perception of the (hypothetical) models involved towards factual knowledge. The article aims to clarify these issues, which influence the ways to conceptualize, perceive, and teach the notion of risk.