Unveiling and unraveling aggregation and dispersion fallacies in group MCDM
This work solves methodological errors in group MCDM for researchers and practitioners, though it is incremental as it builds on existing compositional data analysis.
The paper identifies and addresses three common statistical fallacies in group multi-criteria decision-making (MCDM) when handling priority data, proposing solutions like a compositional aggregation method equivalent to the normalized geometric mean, Bayesian tests for probabilistic ranking, and a tailored clustering algorithm.
Priorities in multi-criteria decision-making (MCDM) convey the relevance preference of one criterion over another, which is usually reflected by imposing the non-negativity and unit-sum constraints. The processing of such priorities is different than other unconstrained data, but this point is often neglected by researchers, which results in fallacious statistical analysis. This article studies three prevalent fallacies in group MCDM along with solutions based on compositional data analysis to avoid misusing statistical operations. First, we use a compositional approach to aggregate the priorities of a group of DMs and show that the outcome of the compositional analysis is identical to the normalized geometric mean, meaning that the arithmetic mean should be avoided. Furthermore, a new aggregation method is developed, which is a robust surrogate for the geometric mean. We also discuss the errors in computing measures of dispersion, including standard deviation and distance functions. Discussing the fallacies in computing the standard deviation, we provide a probabilistic criteria ranking by developing proper Bayesian tests, where we calculate the extent to which a criterion is more important than another. Finally, we explain the errors in computing the distance between priorities, and a clustering algorithm is specially tailored based on proper distance metrics.