Pairwise summation as a method for the additive combination of probabilities in qualitative risk assessments

Qualitative frameworks are widely employed to tackle urgent animal or public health issues when data are scarce and/or urgent decisions need to be made. In qualitative models, the degree of belief regarding the probabilities of the events occurring along the risk pathway(s) and the outcomes is described in nonnumerical terms, typically using words such as Low, Medium, or High. The main methodological challenge, intrinsic in qualitative models, relates to performing mathematical operations and adherence to the rule of probabilities when probabilities are nonnumerical. Although methods to obtain the qualitative probability from the conditional realization of n events are well-established and consistent with the multiplication rule of probabilities, there is a lack of accepted methods for addressing situations where the probability of an event occurring can increase, and the rule of probability P(AUB) = P(A) + P(B) − P(A∩B) should apply. In this work, we propose a method based on the pairwise summation to fill this methodological gap. Our method was tested on two qualitative models and compared by means of scenario analysis to other approaches found in literature. The qualitative nature of the models prevented formal validation; however, when using the pairwise summation, results consistently appeared more coherent with probability rules. Even if the final qualitative estimate can only represent an approximation of the actual probability of the event occurring, qualitative models have proven to be effective in providing scientific-based evidence to support decision-making. The method proposed in this study contributes to reducing the subjectivity that characterizes qualitative models, improving transparency and reproducibility.