Supporting decisions by unleashing multiple mindsets using pairwise comparisons method

Inconsistency in pairwise comparison judgements is often perceived as an unwanted phenomenon and researchers have proposed a number of techniques to either reduce it or to correct it. We take a viewpoint that this inconsistency unleashes different mindsets of the decision maker(s) that should be taken into account when generating recommendations as decision support. With this aim we consider the spanning trees analysis which is a recently emerging idea for use with the pairwise comparison approach that represents the plurality of mindsets (in terms of a plurality of vectors corresponding to different spanning trees). Until now, the multiplicity of the vectors supplied by the spanning trees approach have been amalgamated into a single preference vector, losing the information about the plurality of mindsets. To preserve this information, we propose a novel methodology taking an approach similar to Stochastic Multi-criteria Acceptability Analysis. Considering all the rankings of alternatives corresponding to the different mindsets, our methodology gives the probability that an alternative attains a given ranking position as well as the probability that an alternative is preferred to another one. Since the exponential number of spanning trees makes their enumeration prohibitive, we propose computing approximate probabilities using statistical sampling of the spanning trees. Our approach is also appealing because it can be applied also to incomplete sets of pairwise comparisons. We demonstrate its usefulness with a didactic example as well as with an application to a real-life case of selecting a Telecom backbone infrastructure for rural areas.