Strict Preference Reversal Separates Value States

Abstract

Opposite strict rankings on one option carrier require distinct temporal value states.

Theorem 1.1 (A strict reversal excludes one time-invariant scalar value).

$$\forall U:\mathrm{Type},a,b:U,V_0,V_1:U\to \mathbb{R},(V_0(a)>V_0(b)\wedge V_1(b)>V_1(a))\Rightarrow V_0\ne V_1.$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/DecisionValueScale/StrictPreferenceReversalValueState.strict_preference_reversal_changes_value_state (✓ std3). ∎

Source. Repository-derived.

Commentary.

Both moments use the same option carrier and the same two options. Each moment has a real-valued function that faithfully represents its observed strict ranking.

The first function ranks a above b, while the second ranks b above a. If the functions were equal, asymmetry of the real strict order would give an immediate contradiction.

Their public inequality is exactly the value-state change forced by the source assumptions, and rules out a single time-invariant scalar representation of both moments.

References

• Truth anchor: D5/S3/ConceptDynamics/DecisionValueScale/StrictPreferenceReversalValueState.strict_preference_reversal_changes_value_state