Fixed-Point Paradox: Reason-Responsiveness Simulator

Understanding the ρ-Metric and System Classification

The reason-responsiveness metric (ρ) quantifies how strongly an agent's reasons predict its actions. This is the compatibilist definition of coherent agency from the Fixed-Point Paradox paper (Equation 1).

Random Process (ρ ≈ 0.00): Actions are uncorrelated with reasons. This represents pure indeterminism—not agency.

Compatibilist Agent (0.50 < ρ < 0.90): Actions reliably track reasons, but not deterministically. This is the regime of coherent, reason-responsive agency.

Mechanical System (ρ ≈ 1.00): Perfect correlation. Actions are completely determined by prior state—no room for deliberation.

The FPP proves that counterfactual freedom (CFF) is formally incoherent. The ρ-metric provides the epistemically verifiable, computable alternative: a measurable property of systems that we can call "freedom" without logical contradiction.