A note on analytic hierarchy process group consistency for the row geometric mean priorization procedure

This work analyses the consistency in group decision making for the analytic hierarchy process (AHP). When using the weighted geometric mean method as the aggregation procedure, the row geometric mean method (RGMM) as the priorization procedure, and the geometric consistency index as the inconsistency measure, the paper proves that the inconsistency of the group is smaller than the largest individual inconsistency. This result complements that obtained by Xu for the eigenvector priorization method and its associated consistency index. Moreover, our result guarantees that by using the RGMM priorization procedure, the group priorities obtained through the aggregation of the individual priorities verify the requirement of consistency proposed in AHP methodology if the individual priorities also verify this requirement.