4. Three Costs, One Action

A lasting intelligent system pays three kinds of cost as it acts. Name them plainly:

1. H — Cost of being wrong. Value forgone when choices miss what you care about.
2. C — Cost of model complexity. The price of departing from what you already treat as default (the KL cost from the reference, scaled by τ).
3. K — Cost of changing. The work of moving from one configuration to another as you act and learn—decision motion plus, in the physical world, actuation.

The framework’s action is their sum:

L = H + C + K

A persistent system tends to minimise that sum. The companion book calls the principle Sorter’s Law: minimise predictive error, model complexity, and update cost together—not as three unrelated chores.

Static vs persistent choice

• Choose once, with no time to pass: minimise H + C (a free-energy style objective). The minimiser is the forced Gibbs/Boltzmann choice distribution.
• Act over time: descend that free energy by score-driven relaxation until you rest at the same distribution. Persistence adds K; it does not invent a fourth unrelated law.

Why AI people should feel déjà vu

Write the static objective the other way up:

Maximise expected value under ρ, minus τ times KL(ρ ∥ µ).

That is—slot for slot—the objective of:

• RLHF (reinforcement learning from human feedback): pretrained model as µ, reward model as V, KL coefficient as τ;
• soft reinforcement learning: entropy-regularised policies;
• rational inattention models in economics;
• pieces of active inference in cognitive science.

Slot	Economics (this paper)	RLHF / soft RL	Rational inattention
ρ	Choice pattern	Aligned / soft policy	Stochastic choice
µ	Doxa / reference	Pretrained base / reference policy	Prior before attention
V	Value / payoff	Reward model	Payoff
τ	Info price	KL weight / temperature	Attention cost

The systems now entering the economy as workers and copilots were trained to this objective. At the optimum they satisfy the framework’s equation by construction. The theory of the economy and its newest participants share a form. Alignment problems and economic problems meet in the same two objects: V and µ.

The score is why “irrational” behaviour is often doxic

Score = ∇V/τ + ∇log µ

People move toward what is valuable and toward what is expected. A model that only sees V will call the second term “bias.” The framework calls it the doxic gradient. At high τ (thinking costly), habit and norm dominate. At low τ, calculated value dominates. Real communities live in the mix.

Gauge warning (one careful sentence)

Without independent knowledge of V and τ, you cannot uniquely split observed behaviour into “value” versus “reference”—there is a freedom to move mass between them. Measurement claims need extra handles. The paper treats that honestly; popular talk often does not.

Path cost in one picture

When you act over time, the informational piece of K is the cost of steering away from the reference dynamics—the “path KL.” Steep value landscapes are expensive to climb; flat ones are nearly free. Physical actuation cost is separate domain input (joules, wear, motors)—priced later when humans and robots share one equation.

Next: fill the empty slot that makes the structure economic—the social reading of µ as doxa.