SAPEVO-M (Simple Aggregation of Preferences Expressed by Ordinal Vectors, Multi-Decision-Maker)

SAPEVO-M is a group-ranking method for when a decision is made not by one person but by a committee, and every member can compare criteria and alternatives pairwise on a simple scale. Its output is a numerical score for every alternative and the rank that score produces. SAPEVO-M does not ask for weights from outside; it derives criterion importance too from the decision-makers' own pairwise judgements. The method was proposed by Gomes, de Mello and Costa in 2020 in Pesquisa Operacional, and it extends the single-decision-maker SAPEVO method to group decisions.

The idea behind SAPEVO-M is that a committee giving simple pairwise judgements is more reliable than giving complex numerical assessments. Every member is asked to answer, on a simple seven-level scale, the question "how much more important is criterion A than criterion B" or "how much better is alternative A than alternative B." Unlike methods such as AHP that require a consistency check, SAPEVO-M accepts every member's judgements as they are and combines all members' judgements through row sums.

The philosophical consequence of this structure is that SAPEVO-M is an aggregation method, not a consensus method. Even where members disagree, the method does not call for a round of discussion; every member's vote is standardised and summed separately. This is an advantage where a quick decision is required, but it can conceal deep-seated disagreements among members.

The method proceeds through two main phases, in nine steps.

The criterion-importance phase. Every decision-maker compares the criteria pairwise and gives a judgement on a seven-level scale (between "much more important" and "much less important"). These judgements are placed in a table; every criterion's row sum gives that criterion's relative importance according to that decision-maker. Each decision-maker's own criterion vector is placed between 0 and 1. If a criterion comes out with a value of zero for a decision-maker, a small correction is applied so that this criterion is not left entirely without influence in the total. Finally, all decision-makers' criterion vectors are summed to give a common criterion-importance vector.

The alternative-preference phase. For every criterion, every decision-maker compares the alternatives pairwise and gives a judgement on the same seven-level scale. This means a separate comparison table for every decision-maker and every criterion. Each table's row sums give that decision-maker's alternative-preference vector for that criterion. This vector is also placed between 0 and 1; where a decision-maker sees all alternatives as equal on a criterion (indifference), that vector is left at zero and no artificial preference is added. All decision-makers' standardised vectors are summed for every criterion, forming the alternative-by-criterion matrix.

In the final step, this matrix is multiplied by the common criterion vector from the criterion-importance phase, and every alternative's total score is found. SAPEVO-M ranks the alternatives from the highest score to the lowest.

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

A SAPEVO-M score is the weighted sum of all decision-makers' criterion and alternative judgements; it is not a percentage or a probability. The absolute size of the scores (for example, 4.3 versus 8.5) does not directly express a ratio; it serves only to rank the alternatives relative to one another. The criterion-importance vector is likewise not a probability distribution (a set summing to 1); it is a raw score summed across decision-makers. It cannot be compared with a score computed with a different group of decision-makers or a different alternative set.

Thus instead of writing:

"SAPEVO-M found the best alternative"

the report should read:

"With this committee's criterion and alternative judgements, the alternative with the highest total score is this one; the score is only a summary of this committee and this alternative set"

SAPEVO-M does not work with crisp data but with pairwise ordinal judgements: a judgement that every decision-maker gives for every pair of criteria and every pair of alternatives. DecisionMind currently holds no other data-type extension of this method.

You need at least two decision-makers, the criteria and alternatives to be compared, and a seven-level judgement from every decision-maker for every pair of criteria and every pair of alternatives within each criterion. SAPEVO-M does not ask for criterion weights from outside; it derives them from the decision-makers' own judgements, so it needs no separate weighting step such as AHP, BWM or Entropy. As the number of decision-makers grows, the number of comparisons grows too; if the committee's time is limited, keeping the number of criteria and alternatives small is recommended.

SAPEVO-M suits situations where a decision is made not by one person but by a committee, where members prefer to give simple pairwise judgements rather than complex numerical scores, and where a fast aggregation is wanted. Its typical territory is defence, public procurement and committee-based technology selection; it quickly combines several experts' views without a consistency check.

It should not be used where disagreement among members is itself important information for the decision; SAPEVO-M does not separately report this disagreement while summing the judgements, and an additional analysis is required. If it is important to check whether members' judgements are consistent, a method that computes a consistency ratio, such as AHP, is more suitable. For example, if a member ranks A over B, B over C, and C over A, this contradiction may go unnoticed in SAPEVO-M; AHP would catch such a contradiction.

Committee decision, simple pairwise judgement, fast aggregation → SAPEVO-M

Member disagreement itself must be reported → a separate consensus analysis after SAPEVO-M

Judgement consistency must be checked → AHP

Single decision-maker, numerical decision table → TOPSIS, RAPS, REGIME

SAPEVO-M's most important advantage is its simplicity: decision-makers are not asked for a complex numerical value but for a simple seven-level pairwise judgement, and this is easy to apply even for committee members who are not experts. Because it does not require criterion weighting as a separate step, both importance and preference can be gathered in a single session. It combines several decision-makers' views quickly without waiting for a consistency check; this is an advantage in committee decisions made under time pressure.

Its limitations stem from its aggregation structure. First, deep-seated disagreements among members can be concealed once combined through row sums; if two members vote in exactly opposite directions, these two votes cancel each other out and may not appear in the result at all. Second, the seven-level scale is a coarse judgement; it must be ensured that the scale is understood the same way by all members. Third, SAPEVO-M does not check judgement consistency; a member giving contradictory judgements (ranking A over B, B over C, and C over A) may go unnoticed. Fourth, as the number of decision-makers and criteria grows, the number of pairwise comparisons to be collected grows rapidly (Costa et al., 2022).

The most common mistake is not clearly explaining what the scale means before collecting members' judgements; one member may mean "much better" by "slightly better" while another means something else with the same phrase. A second mistake is forcibly turning a member's indifference across all alternatives on a criterion (seeing them all as equal) into a preference; indifference should be left at zero, with no artificial order added. A third mistake is reading the total score as a percentage; the score is only a relative summary of this committee and this alternative set. A fourth mistake is presenting a single common result without noticing large disagreements among members; if disagreement exists, the report must state it separately.

The governing principle is this:

A SAPEVO-M result is a sum of the pairwise judgements the committee members supplied; if a member's judgement is flawed or understood the scale differently, the result carries this error too.