Calibration Study — Pre-Registration

Status: pre-registered, not yet run Date: 2026-06-01 Unblocks: adaptive agents study (arms 1–3)

Motivation

The adaptive agents study cannot distinguish three causes of a toxicity drop without an external signal:

1. Agents improved quality. (governance worked)
2. Agents rejected more. (filtering)
3. Agents gamed the proxy — v̂ rises while true quality stays flat. (governance defeated)

The framework also rests on the implicit assumption that the proxy-derived p = sigmoid(v̂) is well-calibrated against SoftInteraction.ground_truth (the realized v ∈ {+1, -1} label). That has never been measured. Until both things are anchored, every downstream result is interpretable only at the level of p — which is exactly what a strategic agent will defeat.

Central goal

Produce a triangulated quality signal that adaptive-agent results can be interpreted against:

• a measured proxy-fidelity baseline (p vs ground_truth),
• an external judge anchor (LLM-judge scores on accepted interactions),
• inter-rater agreement across judges (so "the judge is also gameable" is bounded, not waved away).

The deliverable is a CSV of accepted interactions with {v_hat, p, ground_truth, judge_score_claude, judge_score_gpt4o_mini, judge_score_llama, agreement_metrics} that downstream studies can join against by run-id.

Arms

Arm A — Proxy fidelity

Measure how well p = sigmoid(v̂) from ProxyComputer tracks the realized ground_truth label.

• Procedure: generate interactions with a known latent generator probability drawn from a controlled grid (e.g. {0.05, 0.2, 0.4, 0.6, 0.8, 0.95}, ≥500 interactions per bin) and sample ground_truth ∈ {+1, -1} from it. Run ProxyComputer to compute (v_hat, p) per interaction. Bin p, compute the empirical frequency of ground_truth = +1 per bin (reliability diagram).
• Metrics: expected calibration error (ECE), maximum calibration error (MCE), Brier score, reliability-diagram bins.
• Sweep: the sigmoid k parameter; report fidelity vs k. Identify the k that minimizes ECE.
• Output: runs/<ts>_calibration_fidelity/ with per-bin CSV and reliability plot.

Arm B — External judge anchor

Build the un-gameable quality signal the adaptive study needs.

• Procedure: sample a held-out set of accepted interactions from static-baseline runs (≥1000 interactions, stratified across scenarios and p bins). For each interaction, present its content artifact (text/output, not the proxy observables) to an LLM judge with a fixed rubric. Judge returns a score on [0, 1].
• Prompt discipline: the judge prompt MUST NOT include the ProxyObservables fields ProxyComputer reads — concretely: task_progress_delta, rework_count, verifier_rejections, tool_misuse_flags, counterparty_engagement_delta. The judge rates on content quality dimensions orthogonal to those signals. This is what makes the signal un-gameable from an adaptive agent's perspective — the agent can shift observables without shifting what the judge sees.
• Judges: Claude, GPT-4o-mini, Llama 3.x (matches existing Table 9 setup).
• Output: runs/<ts>_calibration_judge/judge_scores.csv with one row per interaction × judge.

Arm C — Inter-rater agreement

Bound the "the judge is also gameable" concern.

• Procedure: on Arm B's sample, compute pairwise agreement across the three judge models.
• Metrics: Krippendorff's α (continuous), Spearman ρ between judge pairs, intra-class correlation (ICC). Report disagreement-by-bin so we see whether judges disagree more at the tails.
• Decision rule: if α < 0.5, the judge ensemble is too noisy to anchor the adaptive study — escalate (add a 4th judge, switch to a stronger model, or fall back to human spot-checks on a smaller subsample). Pre-register the α threshold so we don't drift it post-hoc.

Critical confound

The judge is also a model. A sophisticated adaptive agent could, in principle, learn to game the judge rather than the proxy. Three defenses:

1. The judge prompt rubric is fixed and orthogonal to ProxyComputer's observables, so the gaming channel is not the same one.
2. Inter-rater agreement (Arm C) bounds the size of model-specific exploits — an attack that fools Claude but not GPT-4o-mini and Llama will surface in α.
3. We pre-register an external-quality threshold before the adaptive runs and never tune it afterward. The adaptive study reports judge-rated quality as a held-out signal, not as a target.

These do not eliminate the recursion — they bound it. State the bound explicitly in any downstream finding.

Pre-registered commitments

• p grid, sample sizes, and k sweep range for Arm A are fixed before data collection.
• Judge prompt rubric, judge model versions, and excluded observable features for Arm B will be version-locked at swarm/judges/rubric_v1.md before any Arm B data collection.
• The Krippendorff α decision threshold for Arm C is set in advance.
• The CSV schema downstream studies join against is frozen before the adaptive study begins.
• All judge calls are logged in append-only JSONL alongside the run artifacts for full reproducibility.

Outcomes

• p is well-calibrated AND judges agree (α ≥ 0.7): the strong result. Adaptive study unblocked with confidence; p can be reported as a calibrated proxy; judge serves as the un-gameable anchor.
• p is poorly calibrated but judges agree: the framework still has a usable external anchor; we report the calibration gap honestly and re-tune k. Adaptive study still unblocked.
• Judges disagree (α < 0.5): the anchor itself is too noisy. The adaptive study cannot rely on a single ensemble score. We either add judges, switch models, or fall back to a smaller human-rated subsample. This is itself a publishable result about LLM-judge reliability.
• p well-calibrated AND judges agree with each other, but the proxy and the judge ensemble disagree: p and the external judge measure different things. Most interesting result — interpret carefully; this is where the proxy-gaming threat model lives.

Order of operations

1. Arm A — proxy fidelity on existing static-baseline data (no new runs needed if logs are sufficient). Cheap, runs first.
2. Arm B — build judge pipeline, freeze rubric, run on stratified sample.
3. Arm C — compute agreement on Arm B's output.
4. Freeze the joined CSV schema. Adaptive study (arms 1–3) is unblocked.

Arm A is independent and can begin immediately. Arms B and C share the judge pipeline and are run in sequence.