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Priorities in multi-criteria decision-making (MCDM) convey the relevancepreference of one criterion over another, which is usually reflected byimposing the non-negativity and unit-sum constraints. The processing of suchpriorities is different than other unconstrained data, but this point is oftenneglected by researchers, which results in fallacious statistical analysis.This article studies three prevalent fallacies in group MCDM along withsolutions based on compositional data analysis to avoid misusing statisticaloperations. First, we use a compositional approach to aggregate the prioritiesof a group of DMs and show that the outcome of the compositional analysis isidentical to the normalized geometric mean, meaning that the arithmetic meanshould be avoided. Furthermore, a new aggregation method is developed, which isa robust surrogate for the geometric mean. We also discuss the errors incomputing measures of dispersion, including standard deviation and distancefunctions. Discussing the fallacies in computing the standard deviation, weprovide a probabilistic criteria ranking by developing proper Bayesian tests,where we calculate the extent to which a criterion is more important thananother. Finally, we explain the errors in computing the distance betweenpriorities, and a clustering algorithm is specially tailored based on properdistance metrics.

Unveiling and unraveling aggregation and dispersion fallacies in group MCDM