Weighted Scoring

Weighted scoring combines an option’s scores on several criteria into one total by multiplying each score by a weight and adding the results. With weights written as fractions that sum to 1, a total of 0.50 × 80 + 0.30 × 40 + 0.20 × 60 = 64 lies on the same 0–100 scale as the scores. The UK multi-criteria analysis manual calls this the linear additive model and treats it as the most common form of multi-criteria decision analysis.

A weight is the value of a swing

A weight of 50% does not mean “speed is half of everything.” It means the change from the 0-point anchor to the 100-point anchor on that criterion, say from 7 to 5 minutes per case, is worth half of all such swings combined, and 5/3 of the swing on a 30% criterion. The manual recommends eliciting weights by swing weighting: compare the swing from 0 to 100 on one scale with the swing on another, taking into account both how large the difference is and how much it matters. Change the anchor range and the appropriate weight changes too.

Weights fix exchange rates, which is a useful check. At weights of 50/30/20 on handling time (7 → 5 minutes), monthly cost (800 → 200 units), and administration (20 → 0 hours), one minute per case is 50 × 0.50 = 25 total points. The same 25 points on cost need 25 / 0.30 ≈ 83 score points, or about 500 currency units per month; on administration they would need 125 score points, more than the whole range. If the people who own the work find that exchange wrong, the weights are wrong. Record the elicited weights and who set them where the decision is kept — for an architectural choice, the decision record — because a total whose weights nobody can account for is not reviewable.

What adding assumes

A weighted total inherits uncertainty from its inputs. Record whether each score comes from a measurement, a vendor statement, a trial, or an impression, and estimate a defensible range where possible. A three-point gap is not automatically meaningless: on a 0–100 scale, totals of 73 and 70 with uncertainty bounded at ±0.2 each retain a minimum gap of 2.6 points if weights are fixed. Whether that difference matters in practice is a separate decision. Wider uncertainty or plausible changes in weights can reverse an apparently larger lead. Use sensitivity analysis to test the ordering against those assumptions, retaining the agreed base weights for the reported comparison. If the evidence does not separate the options robustly, report that result and decide whether further evidence is worth collecting. A score structures the trade-off; it does not remove the need to examine the inputs.

A weighted sum is compensatory: a low score on one criterion can be offset by high scores elsewhere. Conditions that must not be traded belong in mandatory gates before scoring, in the same way a constraint is settled before options are compared. Adding also assumes that the preference for a level on one criterion does not depend on the levels of the others, which the manual calls mutual preference independence; when an assessor cannot score one criterion without knowing another, the criteria overlap or interact and should be restructured, or scenarios compared instead.

Check that weights sum to 100% before converting them, and keep the base weights fixed while sensitivity analysis explores alternatives. The term is unrelated to weighted averaging of classification metrics, where weights are class frequencies rather than preferences.

References

• UK Government: Multi-criteria analysis manual

Figures here are illustrative.