PROSA-C (Criteria-Level Sustainability Preference Ranking)

PROSA-C is a method for ranking alternatives when you already hold a numerical decision table. Its output is a score for every alternative and a descending order based on that score. It was proposed by Ziemba in 2019 as a response to the tendency of common MCDA methods, in sustainability assessments, to let strength on one criterion readily paper over weakness on another. Its name comes from the "criteria level" abbreviation; what sets it apart from PROSA-G, its group-level sibling introduced in the same article, is that it measures imbalance criterion by criterion.

PROSA-C's starting point is PROMETHEE II: every alternative receives a net outranking score built from pairwise comparisons, and these scores are summed with weights. Ziemba's objection is this: this summation carries a "weak sustainability" view, that is, it assumes that a good state on one criterion can compensate for a bad state on another. Under a strong sustainability view, however, criteria cannot fully substitute for one another; environmental harm cannot be fully cancelled out by economic gain.

To make this distinction concrete, PROSA-C penalises every alternative's net score with an imbalance term that measures how far its criterion-level flows deviate from its own net score. If an alternative earned its total score by shining on a single criterion, this deviation is large and is subtracted from its score; if it spread its score evenly across criteria, the deviation stays small. The philosophical consequence is that PROSA-C is only partly compensatory. It inherits PROMETHEE II's full compensation but curbs it according to the question "how unbalanced are you across criteria." The larger the sustainability coefficient chosen, the heavier the penalty, and the less compensatory the method becomes.

The method proceeds through four steps.

First, a separate outranking flow for each criterion. On every criterion, an alternative is compared pairwise against all other alternatives; the difference between the comparisons it wins and those it loses, according to that criterion's preference function, is divided by the number of alternatives minus one to give its flow score on that criterion. For cost criteria the sign of this difference is reversed. The preference function can vary from criterion to criterion; its simplest form (classical outranking, "usual") looks only at which alternative's value is larger.

Second, PROMETHEE II's net flow. The criterion-level flows are multiplied by the criterion weights and summed. This is the compensatory score that forms PROSA-C's starting point.

Third, the imbalance measure. For every criterion, the difference between that criterion's flow and the alternative's own net flow is taken, in absolute value, multiplied by that criterion's weight and by the sustainability coefficient set for it, and then summed across all criteria. The sustainability coefficient determines how heavily imbalance on that criterion is penalised; Ziemba's suggested range is 0 to 0.5.

Fourth, penalty and ranking. The imbalance measure is subtracted from the net flow. An alternative that earns its total score from a single criterion loses more than one that spreads the same score evenly.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The PROSA-C score shows both how far an alternative outranks the others and how evenly it achieves that outranking across criteria. The score can be negative; like PROMETHEE II's net flow, the PROSA-C score is not an absolute measure of "goodness" but a relative position within this particular alternative set. Above zero means above average, below zero means below average; it cannot be compared with a score from a different analysis.

A small score gap between two alternatives may rest on which one takes a smaller imbalance penalty; this gap is sensitive to the weights and to the sustainability coefficients.

Thus instead of writing:

"PROSA-C found the most sustainable alternative"

the report should read:

"With these weights and these sustainability coefficients, the alternative achieving the most balanced outranking is this one; the ranking is sensitive to the size of the coefficients"

PROSA-C works with crisp data: one number per cell. You need alternatives in rows, criteria in columns; direction information for every criterion; criterion weights summing to 1; a preference-function type for every criterion (the simplest is "usual," requiring no thresholds); and, for every criterion, a sustainability coefficient between 0 and 0.5. This coefficient is not an optional detail; DecisionMind will not run the method without it being supplied. PROSA-C does not produce weights, it asks for them from outside. DecisionMind currently holds no extension of this method; it works in its base, crisp form.

PROSA-C is a suitable choice if your criteria can be measured numerically and the decision needs to reflect a strong sustainability view, that is, if you do not want a good state on one criterion to fully cancel out a bad state on another. It is typically used in sustainability decisions where environmental, social and economic dimensions are assessed together.

The situation where it should not be used arises when there is no justification for how the sustainability coefficient is to be set. The coefficient draws on both the criterion's weight and a judgement of "how uncompensatable is this criterion"; if the two are set from the same intuition without justification, the method fails to carry the "criteria-level sustainability" distinction its name promises, and collapses into circular reasoning. If the decision is to proceed on a fully compensatory logic throughout, PROMETHEE II on its own suffices; PROSA-C's added complexity is not needed.

A sustainability decision, full compensation between criteria not wanted → PROSA-C

Full compensation accepted, no sustainability emphasis → PROMETHEE II

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

PROSA-C's greatest strength is turning a philosophical concept like "strong sustainability" into a measurable penalty. While preserving PROMETHEE II's pairwise-comparison logic, it explicitly pulls back alternatives that shine on a single criterion. When the sustainability coefficient is set to zero, the method becomes equivalent to PROMETHEE II; this makes PROSA-C a natural extension of the earlier method and makes the difference between the two directly comparable.

PROSA-C's most contested point is that the sustainability coefficient plays a role both independent of and interacting with the criterion weight; if the coefficient and the weight are derived from the same intuition, the method rests on circular justification (Ziemba's own 2019 study stresses that this distinction must be drawn carefully). The method inherits the whole of PROMETHEE II's input burden (preference function, thresholds where needed) and adds a further set of coefficients on top; this makes input preparation heavier than for AHP or TOPSIS. As a generalisation of the base PROSA method (Ziemba et al., 2017), PROSA-C is a relatively new method, and its testing by independent researchers across different sustainability domains (electric-vehicle selection, for instance) is still ongoing (Ziemba, 2020).

The most common mistake is confusing the sustainability coefficient with the "importance weight" and using the same number twice; the weight determines how much a criterion enters the decision, while the coefficient determines how heavily imbalance on that criterion is penalised, and the two answer different questions. A second mistake is pushing the coefficient, without justification, to 0.5 (the suggested upper limit) and turning the method into something close to elimination logic; this takes PROSA-C out of being only partly compensatory, and the report must state this plainly. A third mistake is leaving the choice of preference function and thresholds unjustified, as in PROMETHEE II; this choice also changes the result in PROSA-C. A fourth mistake is reading a negative score as "bad"; the score only shows relative position within this particular alternative set.

The governing principle is this:

A PROSA-C result is a consistent summary of the weights, preference functions and sustainability coefficients you supplied; if the choice of coefficient is contested, the imbalance penalty is contested too, and the report must show this.