The case
World. A hidden state x_t ∈ {safe, dangerous} with known switching. The experimenter sees it; the agent does not.
Processes and actions. A sentry that favours protection when danger is anticipated, and an investigator that favours acquiring diagnostic evidence. Two actions: shelter, which yields an uninformative observation, and inspect, which reveals the state with 90% accuracy at a modest time cost. Inspection is physically safe in the first version, so that a real risk of injury does not confound the question.
Dynamics. b_t the probability of danger, g_t ∈ [0, 1] the sentry’s authority. P(inspect) = σ(βΔV_t − κg_t), with ΔV_t the current expected advantage of inspecting, information value and cost included; the κg term lets the sentry block inspection that is otherwise worth doing. Belief updates on what is observed; authority updates more slowly, g_{t+1} = (1 − η)g_t + η F(b_t, g_t, r_t, d_t), with r reinforcement of protection and d corrective evidence. The manipulation that matters is whether F rewards the sentry on independent evidence of danger or on its apparent success under the policy it chose.
First experiment. Train in danger, then switch to safe.
| condition | authority | diagnostic evidence |
|---|---|---|
| Bayesian baseline | no separate authority state | by ordinary decision cost |
| habit baseline | persistence of the action policy | same opportunities |
| governance model | learned sentry authority | sentry can restrict inspection |
| independent audit | learned sentry authority | external evidence reaches the evaluator |
| protected investigator | learned sentry authority | investigator keeps some guaranteed access |
Measure time to recognize the change, how long protection outlasts recognition, and the cumulative cost of needless protection. The result to look for: a regime in which corrective evidence would suffice to change the appraisal but the governance structure keeps it from becoming consequential.
Factorial version. Governance feedback (authority fixed or independently evaluated / reinforced by success under the dominant regime) × evidence restriction (independent / limited by protective authority) × correction rights (ordinary update / independent audit or protected challenge): eight conditions, a matched habit model and a Bayesian decision-maker, common seeds and event sequences. The tests are interactions: whether authority feedback is especially persistent when it also controls evidence, and whether independent correction removes that. The system must still protect when danger is real.
Measures shared with the other toys. Calibration, diagnostic sampling, authority concentration, authority–evidence responsiveness, exit delay, hysteresis, regulatory cost, recovery of alternatives, task performance, and cumulative avoidable loss against a policy with the same admissible interventions. The diagnostic information available, I(H; O | do(a)), is kept apart from the information sampled and from the information granted influence.
What it can show
Whether the stipulated coupling produces evidence-tracking, inertial, self-confirming or revisable regimes, and where their boundaries lie (a phase diagram), within the model.
What it cannot show
That anxiety or any institution instantiates the mechanism (CLAIM-427). And if a Bayesian learner with matched information costs, or a habit model with matched memory, reproduces every intervention response, the extra authority state has not earned its place. That outcome is to be reported, not tuned away.
Neighbours named in the exchange
The exchange also sketched an emergency agency (actual threat T, authority g, resources r, an agency that influences when an emergency is declared over), CASE-144’s evaluator study, a supervisor-against-local- accommodation design for CLAIM-358 (CASE-109), an agenda-controlled Condorcet cycle (CLAIM-448), and a protected industry (CLAIM-445). It named off-the-shelf starting points, none of which implements the abstraction: the Tiger POMDP in pomdp_py, pymdp for an active-inference comparison, Mesa, NetLogo’s Rebellion model (private grievance against public behaviour under policing), PettingZoo and Gymnasium’s FrozenLake.
Note of 2026-10-25: proposed again, and partly run
A30’s two-specialist experiment and A31’s Experiment 1 (“captured evaluator”), in the exchange of 2026-10-24, continued, re-propose this case without citing it. Each has a specialist better before an environmental shift and the other after it, avoidance that yields the same feedback in both states, and a 2×2 of evidence access (protected against selective) by scoring (fixed against authority-dependent). The two axes are CLAIM-404’s two routes, evidence received and criteria of weighing. A31’s reading of the outcome: “If guaranteed evidence access resolves lock-in, but changing the evaluation criteria adds nothing, the result favors an exploration explanation.” CASE-157’s extension (run 2026-10-25) found each route sufficient alone, in one parameterization with binary decisions. A31 adds baselines (selection-aware Bayesian learning, a contextual bandit, the replicator and a history-dependent gate) and a variant in which unused specialists deteriorate. As partial monitoring, the case’s game is locally observable, so what fails is access, not observability (CLAIM-446’s note of 2026-10-25, the approach–avoid game). The case is unchanged.