Decision Sufficiency Without Full Prediction

Abstract

One constant concept determines every optimal action without determining full payoffs.

Theorem 1.1 (Decision sufficiency does not require full prediction).

$$\mathrm{Refines}\left(optimalActions,constantConcept\right)\wedge \neg \mathrm{Refines}\left(fullPayoffProfile,constantConcept\right).$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/DecisionValue/DecisionWithoutFullPrediction.decision_sufficiency_without_full_prediction (✓ std3). ∎

Source. Repository-derived.

Commentary.

The source has two states and two actions. Action a pays 10 and 100 at the respective states, while action b pays 0 and 1.

The optimal-action concept is constructed as the set of actions whose payoff dominates every alternative. The full-result target records the complete action-payoff profile, and the concept readout is constant.

Both optimal-action sets equal {a}, so the first target factors through the constant concept. The two full profiles differ at action a, so the second target cannot factor through that same concept.

References

• Truth anchor: D5/S3/ConceptDynamics/DecisionValue/DecisionWithoutFullPrediction.decision_sufficiency_without_full_prediction
• Dependency: D5/S3/ConceptDynamics/ConceptJoinUniversal