The Legitimacy Equation

Definition

The Legitimacy Equation is a formal expression of how stable, trustworthy meaning behaves under pressure. It models legitimacy as:

L = (T × P × C) ÷ D

Where:

• T = Truth Integrity (truth fidelity)

• P = Power Alignment (how authority responds to truth)

• C = Coherence Coefficient (how structure conducts meaning)

• D = Drift Index (pressure, entropy, and accumulated distortion)

• L = Legitimacy (the stability and reliability of the meaning system)

The equation states that legitimacy increases when truth, power, and coherence move together and decreases as drift outgrows them.

Conceptual Role

The Legitimacy Equation is the primary quantitative expression used in Moral Physics and Meaning System Science to:

• make legitimacy measurable

• quantify drift and coherence

• compare systems under different levels of pressure

• analyze why some transformations hold while others quietly fail

It turns “trust” and “credibility” from vague impressions into a structured, analyzable function.

Relationship to the Law of Moral Proportion

The Law of Moral Proportion describes how legitimacy behaves as a proportional function of T, P, C, and D.
The Legitimacy Equation is the mathematical form of that law:

Law of Moral Proportion → principle
Legitimacy Equation → equation expressing that principle

The equation is how the law is instantiated in diagnostics, models, and measurement.

Variables in the Equation

• Truth Integrity (T)
  How accurately reality is perceived, verified, and carried into communication and decision-making.

• Power Alignment (P)
  How proportionally authority, leadership, and signals respond to verified truth.

• Coherence Coefficient (C)
  How well structure, roles, and processes conduct meaning with clarity, accountability, and continuity.

• Drift Index (D)
  The degree of accumulated distortion, overload, contradiction, and entropy acting on the system.

• Legitimacy (L)
  The resulting stability, trustworthiness, and reliability of the meaning structure over time.

Interpretive Use

The Legitimacy Equation allows leaders and practitioners to ask:

• Are we growing truth faster than we grow drift?

• Are power and structure actually adjusting to what we know?

• Is our coherence strong enough to carry what we’re asking people to hold?

• Are we burning legitimacy faster than we can restore it?

It moves the conversation from blame and personality to proportion and structure.

Relationship to Transformation Science and Transformation Management

In Transformation Science, the Legitimacy Equation is used to:

• interpret failure modes in transformation

• understand legitimacy crises

• identify where T, P, C, or D are out of proportion

• forecast risk in AI-accelerated environments

In Transformation Management, it underpins:

• the Legitimacy Diagnostic Protocol (LDP-1.0)

• the 3E Standard™ criteria

• structural drift and coherence assessments

• proportional design of governance and operating rhythm

Applications

The Legitimacy Equation is applied in:

• diagnosing systemic drift before visible breakdown

• reading organizational politics as structural imbalance

• analyzing trust erosion in institutions

• understanding burnout as a symptom of structural proportion failure

• designing transformations that conserve, rather than consume, legitimacy