Robust weighted aggregation of expert opinions in futures studies

Expert judgments are widespread in many fields, and the way in which they are collected and the procedure by which they are aggregated are considered crucial steps. From a statistical perspective, expert judgments are subjective data and must be gathered and treated as carefully and scientifically as possible. In the elicitation phase, a multitude of experts is preferable to a single expert, and techniques based on anonymity and iterations, such as Delphi, offer many advantages in terms of reducing distortions, which are mainly related to cognitive biases. There are two approaches to the aggregation of the judgments given by a panel of experts, referred to as behavioural (implying an interaction between the experts) and mathematical (involving non-interacting participants and the aggregation of the judgments using a mathematical formula). Both have advantages and disadvantages, and with the mathematical approach, the main problem concerns the subjective choice of an appropriate formula for both normalization and aggregation. We propose a new method for aggregating and processing subjective data collected using the Delphi method, with the aim of obtaining robust rankings of the outputs. This method makes it possible to normalize and aggregate the opinions of a panel of experts, while modelling different sources of uncertainty. We use an uncertainty analysis approach that allows the contemporaneous use of different aggregation and normalization functions, so that the result does not depend on the choice of a specific mathematical formula, thereby solving the problem of choice. Furthermore, we can also model the uncertainty related to the weighting system, which reflects the different expertise of the participants as well as expert opinion accuracy. By combining the Delphi method with the robust ranking procedure, we offer a new protocol covering the elicitation, the aggregation and the processing of subjective data used in the construction of Delphi-based future scenarios. The method is very flexible and can be applied to the aggregation and processing of any subjective judgments, i.e. also those outside the context of futures studies. Finally, we show the validity, reproducibility and potential of the method through its application with regard to the future of Italian families.