Manager’s and citizen’s perspective of positive and negative risks for small probabilities

So far „risk‟ has been mostly defined as the expected value of a loss, mathematically PL, being P the probability of an adverse event and L the loss incurred as a consequence of the event. The so called risk matrix is based on this definition. Also for favorable events one usually refers to the expected gain PG, being G the gain incurred as a consequence of the positive event. These “measures” are generally violated in practice. The case of insurances (on the side of losses, negative risk) and the case of lotteries (on the side of gains, positive risk) are the most obvious. In these cases a single person is available to pay a higher price than that stated by the mathematical expected value, according to (more or less theoretically justified) measures. The higher the risk, the higher the unfair accepted price. The definition of risk as expected value is justified in a long term “manager‟s” perspective, in which it is conceivable to distribute the effects of an adverse event on a large number of subjects or a large number of recurrences. In other words, this definition is mostly justified on frequentist terms. Moreover, according to this definition, in two extreme situations (high-probability/low-consequence and low-probability/high-consequence), the estimated risk is low. This logic is against the principles of sustainability and continuous improvement, which should impose instead both a continuous search for lower probabilities of adverse events (higher and higher reliability) and a continuous search for lower impact of adverse events (in accordance with the fail-safe principle). In this work a different definition of risk is proposed, which stems from the idea of safeguard: (1Risk)=(1P)(1L). According to this definition, the risk levels can be considered low only when both the probability of the adverse event and the loss are small. Such perspective, in which the calculation of safeguard is privileged to the calculation of risk, would possibly avoid exposing the Society to catastrophic consequences, sometimes due to wrong or oversimplified use of probabilistic models. Therefore, it can be seen as the citizen‟s perspective to the definition of risk.