SCIENCE · INVESTIGATE AND EXPLAIN

Separate scientific forecasts from value choices in a score

Environmental decisions often compare pollution reduction, water use and cost. Science can inform predicted outcomes and uncertainty, but it does not uniquely determine how stakeholders should value them. A composite score should expose its normalization, weights and any assumption that one benefit can compensate for another harm.

Learning outcome: Find a ranking reversal while holding outcome forecasts fixed. Then impose a hard water-use limit 20 units and explain why B becomes infeasible regardless of its composite score.

Starting recap

Preserve packet identity, independent units, analysis recipe, outcome constraints and review authority; distinguish scientific uncertainty from stakeholder value choices.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

At pollution weight 0.5 and water share of the remainder 0.5, weights are 0.5,0.25,0.25. A score 0.3+1/6+0.1375≈0.60417 exceeds B0.5. At pollution weight 0.75 with the same split, A≈0.60208 falls below B0.75.

Open the experiment

Predict

A ranking reversal caused only by changed weights indicates:

Your prediction and reason

Experiment

Find a ranking reversal while holding outcome forecasts fixed. Then impose a hard water-use limit 20 units and explain why B becomes infeasible regardless of its composite score.

Expose value weights in a multi-criterion comparison

Worked teaching model · synthetic values · Two original candidates: A reduction 30,water use 10,cost 90; B reduction 50,water use 30,cost 200 in fixed comparable units. Scores normalize pollution by 50, water desirability 1−use/30, cost desirability 1−cost/200. Pollution weighta; water(1−a)b; cost(1−a)(1−b). Bounds and linear compensability are stated value choices, not scientific facts.

Weight on pollution reduction: 0.5 fraction Water share of remaining weight: 0.5 fraction

Reset keeps your prediction, captures and practice history.

Original synthetic system; units differ by row
Quantity	Value	Unit
Pollution weight	0.5	fraction
Water weight	0.25	fraction
Cost weight	0.25	fraction
Candidate A composite score	0.6041667	normalized score
Candidate B composite score	0.5	normalized score
A minus B score	0.1041667	normalized score

Scientific predictions and value weights play different roles in a composite ranking.

Normalization anchors and compensability can change rankings even when the physical forecasts do not. Hard environmental or equity constraints should be checked before allowing a good score to compensate for an unacceptable outcome.

Predict, change one control, and retain contrasting captures. Reconstruct the analysis and decision rule before opening feedback. Display precision is not measurement precision.

Scientific predictions and value weights play different roles in a composite ranking.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Define the decision and evidence boundary

Reconstruct the transparent method

The fictional A option reduces 30 pollution units, uses 10 water units and costs 90; B reduces 50, uses 30 and costs 200. Pollution score is reduction/50, water desirability is 1−use/30 and cost desirability 1−cost/200. Those anchors are declared conventions, not physical constants.

Interpret the comparison

Pollution weight is a; water receives(1−a)b and cost(1−a)(1−b), so the three sum to one. A score is 0.6 a+(2/3)waterWeight+0.55 costWeight; B score is a. Changing weights can reverse the ranking without changing any physical forecast. A sensitivity analysis should show where this occurs.

Predeclare limitations and revision

Hard water, habitat, equity or legal constraints may rule out an option regardless of its score. Linear weighting also assumes compensability and independence of value contributions; different stakeholder groups may reasonably reject those assumptions. Report the separate outcomes alongside the score rather than hiding disagreement in a single number.

Worked original packet

Investigation

Find a ranking reversal while holding outcome forecasts fixed. Then impose a hard water-use limit 20 units and explain why B becomes infeasible regardless of its composite score.

Changed-case transfer

At pollution weight 0.25 and all remaining weight on cost, calculate both scores.

Feedback

Weights 0.25,0,0.75 give A0.15+0.4125=0.5625 and B0.25. This is a result of explicit value choices, not proof that A is objectively best for everyone.

Sources and evidence boundary

Original prose, dataset and numerical exercises. Primary method/mechanism source, checked 30 October 2026. The versioned packet is synthetic, not observed fieldwork. No treatment implementation, site access, pollutant handling or real management authorization is requested. Preserve first reasoning and critique in the course workspace.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

At pollution weight 0.25 and all remaining weight on cost, calculate both scores.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Compare cost efficiency without losing total-service constraints Next: Predeclare review triggers across repeated observations

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