PROMETHEE VI (Brans & Mareschal, 1995)

An organisation's R&D committee is assessing three projects. There are three criteria: expected scientific-contribution score, feasibility score and team-readiness score; all three are benefit criteria. The committee has set the weights at 0.4, 0.3 and 0.3, but these weights were formed through discussion rather than a vote, and are not exact.

The method first computes the baseline net flow with the stated weights.

Then every criterion's weight is shifted in turn by ±0.05, the remaining weights are rescaled proportionally, and the net flow is recomputed for each of these six scenarios. Every project's lowest and highest value forms an interval.

The result reads as follows. None of the three intervals overlap with one another: even P2's lowest value (0.25) is above P3's highest value (-0.02), and P3's lowest value (-0.18) is below P1's highest value (-0.10). The ranking P2, P3, P1 is robust against a ±0.05 change in the weights; even if the committee does not know these three criteria's weights exactly, the order does not change.

The committee's hesitation: what happens if the band is widened from ±0.05 to ±0.15? Rerunning the same calculation independently, P1's interval (-0.50; 0.10) and P3's interval (-0.34; 0.14) now overlap; P2's interval (0.15; 0.45) still remains separate. This shows that P2's first place is robust even under wide uncertainty, but the second-third order between P1 and P3 becomes contested under a larger uncertainty in the weights.

In the report: "With the stated weights and a ±0.05 uncertainty band, P2 is clearly first, P3 second, P1 third; since the intervals do not overlap, this order is robust against the choice of weights."

Source: DecisionMind's validation example prepared for the PROMETHEE VI engine. It is based on Brans and Mareschal's (1995) weight-sweep method and is not the paper's own figures. The baseline net flow, the intervals and the ±0.15 band scenario were computed by independently running the engine.

An examinations body is to decide at which campus to hold a national examination. There are three criteria: capacity score, transport-accessibility score and security-infrastructure score; all three are benefit criteria. The weights were set by an internal survey, and the survey itself did not yield an exact number; it only suggested an approximate distribution.

The method first ranks the three campuses with the stated weights, then produces a net-flow interval for every campus by shifting the weights by small amounts. Suppose the highest-capacity campus's interval overlaps with the interval of the campus with the strongest security infrastructure; the order between the two then depends on which criterion is considered slightly more important.

The body's hesitation: if the order between two campuses is this sensitive to the choice of weights, the decision should be supported not by net flow alone but by an additional criterion (such as past examination experience). The position of the third campus, whose interval does not overlap with the others, is beyond dispute.

In the report: "Because two campuses' net-flow intervals overlap, the order between them depends on the choice of weights; the third campus's position is not affected by this uncertainty."

Reporting only the midpoints (-0.20; 0.30; -0.10) in the R&D table and never showing the intervals: this looks, on the surface, no different from base PROMETHEE's single-point result, and the robustness information that is the method's real contribution is lost. The second error is choosing the weight band unjustifiably wide (for instance ±0.40) on the grounds that it "covers every possibility"; this makes almost every ranking look "hard" and misleads the decision maker. The third error is reporting the order between two projects whose intervals overlap in certain language, such as "P3 is strictly ahead of P1"; when there is overlap, the order is not certain.