Decision matrices, uncertainty and comparing alternatives

Separate mandatory conditions from preferences

A mandatory constraint is a condition a candidate must satisfy. Screen those conditions before awarding preference points. A carrier that cannot retain the defined tool set does not become acceptable because it is cheap. If evidence of compliance is missing, record that as unresolved rather than silently marking a pass.

For feasible candidates, list criteria that matter to the decision: task performance, cost, cleaning effort or repair access. Avoid counting the same benefit twice, such as using both empty mass and a carrying-effort rating without examining their overlap. State who chooses the criteria and how conflicting stakeholder priorities will be resolved.

Make the arithmetic and value judgements inspectable

A simple weighted sum multiplies each criterion score by its weight and adds the products. Weights sum to one in our example. Scores must face the same direction, with a higher score consistently meaning more desirable. A cost in euros cannot simply be added to a time in seconds; a defined value scale is needed first.

In this constructed discussion, the team adopts 0–5 value scores. A has cost score 4 and use score 2; B has cost score 2 and use score 5. These are assumed preference ratings, not raw measurements. A real record would retain the prices, task observations and agreed scoring anchors behind them. Treating one score step as having the same value everywhere is an additional assumption of this simple method.

Let w be the weight placed on cost, leaving 1 − w on use. A’s score is 4w + 2(1 − w) = 2 + 2w. B’s is 2w + 5(1 − w) = 5 − 3w. The figure shows how the recommendation changes with a preference, even though the candidate evidence is held fixed.

Ask what new evidence could change the decision

Sensitivity analysis changes an uncertain input or assumption to see whether the decision changes. At cost weight 0.40, B scores 3.8 and A 2.8. But suppose B’s use score is uncertain between 3 and 5. Its total then ranges from 2.6 to 3.8 at that weight, crossing A’s total. The apparent winner is not robust to that uncertainty.

Instead of arguing about an extra decimal place, investigate the disputed use evidence. A short task trial might distinguish the alternatives more usefully than another meeting. More information also consumes time and resources, so match the investigation to the consequence and likelihood of changing the decision.

Keep the original raw criteria beside the totals. Report which candidates remain close, what is unquantified, and why any recommendation differs from the top score. An unexplained exception can reveal that the scoring model omitted an important concern.

Find the preference at which the ranking changes

Set the two totals equal: 2 + 2w = 5 − 3w. Add 3w to both sides and subtract 2, giving 5w = 3, so w = 0.60. At that weight both candidates score 3.2.

At w = 0.80, A scores 3.6 and B 2.6. At w = 0.40, A scores 2.8 and B 3.8. Neither ranking is a universal property of the carriers: the difference follows from the chosen preference weights and the assumed scores.

Try the reasoning

1. Can a high total compensate for failing a mandatory containment requirement?

   Show the answer and reasoning

   No. That requirement is a feasibility condition. Its failure must be resolved rather than traded away through unrelated preference points.

2. Why keep the raw evidence behind a use score?

   Show the answer and reasoning

   A score compresses observation and judgement. The underlying evidence lets reviewers challenge its meaning, uncertainty and comparability.

3. At w = 0.40, does B remain preferred if its use score falls to 3?

   Show the answer and reasoning

   No. B becomes 0.40 × 2 + 0.60 × 3 = 2.6, below A’s 2.8. The uncertain use evidence can reverse the recommendation.

What to carry forward

Show criteria, scales, weights and uncertainty alongside any total. Test the conclusion before calling one alternative best.