check-dominance

Purpose

Identify Pareto-dominated and non-dominated alternatives under strict dominance.

Input contract

required: [alternative_set, score_matrix, criterion_directions]
optional: [missing_value_policy, equality_tolerance]
constraints: [all compared scores share declared direction and scale]

Procedure

1. Normalize criterion direction and validate comparable rows.
2. Compare each ordered pair: no worse on every criterion and strictly better on at least one.
3. Record each dominated alternative with its dominator and witness criterion.
4. Return the non-dominated front and unresolved comparisons.

Output contract

produces: [dominance_relations, dominated_set, nondominated_front, comparison_gaps]
delta_fields: [findings, evidence_updates, uncertainties]

Quality gates

• Every dominated label names a dominating alternative and strict witness.
• No alternative is both dominated and on the non-dominated front under the same tolerance.
• Missing or incomparable scores are never treated as dominance.

Parameterization

Caller supplies alternative schema, criterion direction, tolerance, missingness policy, and whether strict or weak dominance is allowed.

Failure and counterexamples

Reject dominance claims when a criterion direction is unknown or a strict improvement cannot be exhibited.

Provenance map

• resolved: dominance-check

Preserved source criteria ledger

source	criterion
dominance-check	Dominance means no worse on all criteria and strictly better on at least one.
dominance-check	Each dominated determination specifies the dominating alternative.