The use of the geometrical mean for the collection of different
judgments is fundamental, because it has been demonstrated
(IMO, 2002) that its use minimizes the inconsistency of the comparison matrix C (see forward), for the reason that the unanimity
and homogeneity properties are respected. The unanimity property states that, when all the experts give the same judgment x,
the resulting overall judgment should be x. The homogeneity property states that when individuals give a judgement u times larger
than another, the resulting overall judgment should be u times larger too. A mathematical formulation of the unanimity and homogeneity properties is reported in (2) and (3)