Methods · Outranking
PAMSSEM II (Complete-Ranking Variant)
PAMSSEM II uses the same concordance and flow calculation as PAMSSEM I, but at the end places every alternative in order by its net flow; it leaves no incomparable pair, always producing a complete ranking.
Base method's data type: Classical
What Is the Method?
PAMSSEM II is an outranking method for placing alternatives ("which supplier", "which project", "which region") into a single ranking from start to finish, once you hold a decision table scored on several criteria. It shares the same concordance, discordance and flow calculations as PAMSSEM I; its only difference lies in the final step. Where PAMSSEM I can leave some pairs incomparable, PAMSSEM II does not accept this uncertainty and gives a complete ranking, from top to bottom, by net flow. For this reason, DecisionMind also holds the default indifference and preference thresholds tighter in PAMSSEM II than in PAMSSEM I, aiming for a finer gradation of local comparisons when a complete ranking is at stake.
The Philosophy Behind It
PAMSSEM II's underlying idea is to step back from PAMSSEM I's honesty and prioritise decisiveness. In real life, a decision-maker usually has no tolerance for the answer "I cannot decide about these two"; a project must be chosen, a contract must be signed with one supplier. PAMSSEM II meets this need: it takes alternatives through the same concordance and flow calculation, and however close they may be, orders them from largest to smallest by net flow.
This choice carries a cost. A pair left incomparable in PAMSSEM I in fact reflects a genuine tension in the data, one good in one direction, the other good in another. PAMSSEM II disregards this tension, reduces it to a single figure (net flow), and produces an order however small the gap between figures may be. The method therefore gives a decisive but sometimes more certain-looking result than it should.
How It Works
The method follows the same seven steps as PAMSSEM I; it differs only in the last step.
First, pairwise local comparison. For each criterion, the difference between two alternatives is computed and signed according to the criterion's direction. DecisionMind, by default in PAMSSEM II, uses a non-zero indifference threshold and a below-one preference threshold at this step; this gives a more gradual transition than PAMSSEM I's default extreme thresholds (a fully sharp cut-off).
Second, concordance. Local comparisons are weighted-summed using the criterion weights.
Third, discordance. For each criterion, the ratio of the lost difference to that criterion's range in the table is computed.
Fourth, comprehensive outranking degree. If a veto threshold has been specified and a reverse difference on one criterion exceeds it, outranking is reset to zero; if not specified, the comprehensive outranking degree stays directly equal to the concordance degree.
Fifth, outgoing and incoming flow. Each alternative's average outranking and average being-outranked are computed.
Sixth, net flow. Incoming flow is subtracted from outgoing flow.
Seventh, complete ranking. Unlike PAMSSEM I, no comparison is left pending at this step; alternatives are ranked directly from largest to smallest by their net flows.
The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.
How to Read the Output
Net flow shows how far an alternative stands out from the others on average; it is not a percentage or a degree of certainty. The ranking PAMSSEM II produces is always complete, but this completeness looks equally certain even where the gap between two alternatives is small. If two alternatives' net flows differ by only 0.01, this gap appears in the ranking table exactly as "first, second," the same way a pair separated by a gap of 0.30 would.
Thus instead of writing:
"PAMSSEM II found the best alternative with certainty"
the report should read:
"With these weights and thresholds, the top-ranked alternative by net flow is this one; the smallness of the gap should also be reported, because the complete ranking hides it"
Data Type and Inputs
PAMSSEM II works with crisp data: one number per cell. DecisionMind holds no separate data-type extension of this method; it stands alone in its base form.
You need: alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; criterion weights summing to 1; and indifference and preference thresholds (if unspecified, DecisionMind uses default values specific to PAMSSEM II). The veto threshold is optional; if unspecified, no criterion can apply a veto. PAMSSEM II does not produce weights, it takes them from outside.
When to Use It, When Not To
PAMSSEM II is a sound choice if your criteria are numerical, you can accept limited compensation, and the decision-maker genuinely needs a complete ranking, first, second, third.
It should not be used in the following cases: if you want the genuine uncertainty between two alternatives to remain visible in the report (PAMSSEM I is more honest here), if you cannot justify the veto threshold, or if full compensation is acceptable, in which case a simpler method is sufficient.
A complete ranking is essential, limited compensation and veto are optional → PAMSSEM II
Visible uncertainty is wanted → PAMSSEM I
Full compensation acceptable, no veto needed → TOPSIS, SAW
Weights, not thresholds, are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)
Strengths
PAMSSEM II's greatest strength is decisiveness: it resolves the uncertainty PAMSSEM I leaves in some pairs and always produces a usable, complete ranking. Combining the concordance, discordance and veto mechanism with a PROMETHEE-style net-flow calculation offers a richer intermediate computation than methods relying on a single logic alone. It gives the decision-maker the clarity needed to move to the next step, such as signing a contract.
Weaknesses
Its limitations share the same root as PAMSSEM I's, but the preference for decisiveness adds a new risk. First, the result depends directly on the indifference, preference and veto thresholds. Second, if the veto threshold is unspecified, the method quietly falls out of service. Third, and specific to PAMSSEM II, even when net flows are very close to one another, the method still turns this into a complete ranking; this hides the "mixed signal" situation that PAMSSEM I leaves visible, and can make the result look more certain than it is. Fourth, the common limitation of outranking methods applies here too: when the alternative set changes, the ranking can be affected (Roy, 1991).
Common Mistakes
The most common mistake is reading a complete ranking as "equally reliable whatever the gap"; how close the net flows are to one another should be reported separately.
A second mistake is assuming, without ever specifying a veto threshold, that the method will automatically eliminate poor alternatives. A third is confusing PAMSSEM I and PAMSSEM II as the same method and forgetting that the two use different default thresholds; the same data can produce different local-comparison results in the two methods. A fourth is presenting a result from a single weight scenario as certain, without seeing that a small change in the weight distribution could overturn the complete ranking from top to bottom.
The governing principle is this:
A PAMSSEM II result is always a complete ranking, but this completeness does not remove the uncertainty in the data, it only makes it invisible; if the gap between net flows is small, the report must say so explicitly.
Cases
Each case opens with a decision table, describes in words what the method does to it, and shows how to read the result.
1. IT: Choosing among three cloud providers (DecisionMind's validation example)
An IT company will migrate to one of three cloud providers (A1, A2, A3). Three criteria have been set: a service-quality score, a flexibility score and a support score; all three are treated as "more is better". Weights have been set at 0.40 for service quality, 0.30 for flexibility and 0.30 for support. The company has not specified a veto threshold.
| Provider | Service quality | Flexibility | Support |
|---|---|---|---|
| A1 | 3 | 2 | 5 |
| A2 | 1 | 5 | 4 |
| A3 | 4 | 3 | 3 |
| Direction | more is better | more is better | more is better |
| Weight | 0.40 | 0.30 | 0.30 |
The method carries out pairwise local comparisons on each criterion, builds the concordance degree and, since no veto threshold has been given, sets the comprehensive outranking degree directly equal to the concordance degree. Each provider's net flow is then computed and turned directly into a complete ranking.
| Provider | Net flow | Rank |
|---|---|---|
| A3 | 0.10 | 1 |
| A1 | 0.00 | 2 |
| A2 | -0.10 | 3 |
The result reads as follows. A3 has the highest service quality and the highest support; this places it ahead in net flow. A2 is best on flexibility but has the lowest score on service quality, the most heavily weighted criterion, and finishes last. PAMSSEM II has placed all three providers into a complete ranking without leaving any pair pending.
The company hesitates here: what happens if the service-quality weight is lowered from 0.40 to 0.30 and the flexibility weight raised from 0.30 to 0.40? Re-running the DecisionMind engine changes the order completely, to A2, A3, A1; the net flows become 0.10 for A2, -0.10 for A3 and 0.00 for A1. In other words, once the heaviest weight shifts to flexibility, A2, which has the lowest service quality in the table, moves to first place. PAMSSEM II gives a complete ranking under both scenarios, but the two rankings are nearly the reverse of one another.
In the report: "Under the given weights, A3 is first by net flow (0.10); once the service-quality and flexibility weights are swapped, first place passes to A2, so the complete ranking is highly sensitive to the weight distribution."
Source: The table is a teaching validation example prepared by DecisionMind for the PAMSSEM II engine, not a case taken from a paper. The manifest's founding-source record points to a goal-programming paper (Martel and Aouni); that paper's title does not match PAMSSEM's outranking structure, and the DecisionMind team is reviewing this record. This card relies on the verified paper by Ben Amor, Jabeur and Martel (2007) for the method's history.
2. Museums: Tendering a new exhibition-hall design
A state museum will choose among three design-firm proposals. Three criteria have been set: exhibition-space usage efficiency, a projected visitor-experience score and delivery time (inverted, a short time is good). The museum has set a veto threshold requiring that no proposal exceed a given upper limit on delivery time.
The method compares the three proposals pairwise, builds the concordance degrees and checks the veto threshold. Suppose one proposal crossed the veto threshold on delivery time; this proposal can never outrank any of the other proposals, even with the highest visitor-experience score. The remaining two proposals are placed into a complete ranking by their net flows.
The museum hesitates here: the eliminated proposal's visitor-experience score was genuinely very high; would the result change if the delivery-time threshold were relaxed slightly? The complete ranking PAMSSEM II produces depends on how tightly the veto threshold is held, and this threshold must be justified.
In the report: "The proposal exceeding the delivery-time threshold has been eliminated; the remaining two proposals have been placed into a complete ranking by net flow, and the threshold value rests on the museum's contractual schedule."
3. Food Safety: Choosing a wholesale food inspection firm province-wide
A municipality will choose one of three tender proposals from firms that will inspect wholesale food markets. Three criteria have been set: number of inspectors, reporting speed and service fee (inverted, a low fee is good). The municipality has not specified a veto threshold.
The method compares the three proposals and computes net flows, producing a complete ranking. Suppose the result placed first a firm that does not have the lowest service fee but performs consistently well on number of inspectors and reporting speed.
The municipality hesitates here: if the gap between net flows is small, for instance only a few percentage points from the second firm, this small gap appearing as "definite first place" in the complete ranking can be misleading. The municipality should also present the size of the gap between the first and second firms to the council.
In the report: "The firm ranked first by net flow stands out for its consistent performance on number of inspectors and reporting speed; the net-flow gap to the second firm should also be reported."
4. What Not to Do
In the same cloud-provider table, reporting "the method eliminated poor alternatives" without ever setting a veto threshold would be wrong; since no threshold was given, no elimination took place at all. A second error is presenting the small net-flow gap (0.10) between A1 and A3 without seeing it, as "A3 is a clear winner." A third error is reporting a single weight scenario as the final truth without testing that swapping the weights nearly reverses the ranking.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/pamssem-ii
Ben Amor, S., Jabeur, K., & Martel, J.-M. (2007). Multiple criteria aggregation procedure for mixed evaluations. European Journal of Operational Research, 181(3), 1506-1515. DOI: 10.1016/j.ejor.2005.11.048
Roy, B. (1991). The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31(1), 49-73. DOI: 10.1007/BF00134132
Ben Amor, S., & Martel, J.-M. (2014). A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations. European Journal of Operational Research, 238(1), 358-370. DOI: 10.1016/j.ejor.2014.03.036
Martel, J.-M., & Aouni, B. (1990). Incorporating the decision-maker's preferences in the goal-programming model. Journal of the Operational Research Society, 41(12), 1121-1132. DOI: 10.1057/jors.1990.179. (The manifest had recorded a different year and title as the founding source; this card, based on the "PAMSSEM ancestor" note in the kernel code, lists the genuine Martel-Aouni paper carrying the correct year and DOI. The paper is a goal-programming study and does not directly define PAMSSEM's outranking structure.)