Checking the Consistency of Solutions in Decision-Making Problems with Multiple Weighted Agents

A decision-making problem diffused in various practical contexts is that of aggregating multi-agent judgements into a consensus ordering, in the case the agents' importance is expressed through a set of weights. A crucial point in this aggregation is that the consensus ordering well reflects the input data, i.e., agents' judgements and importance. The scientific literature encompasses several aggregation techniques, even if it does not include a versatile tool for a quantitative assessment and comparison of their performance. The aim of this paper is introducing a new indicator (p), which allows to verify the degree of consistency between consensus ordering and input data. This indicator is simple, intuitive and independent from the aggregation technique in use; for this reason, it can be applied to a variety of practical contexts and used to compare the results obtained through different aggregation techniques, when applied to a specific problem. The description is supported by various application examples