Why

The reasoner-agnostic martingale program needs humans whose beliefs update — but human studies are deferred, so we simulate them with LLMs. This page records what makes an LLM-simulated human useful for belief-update / sycophancy studies: how to give it a prior, a confirmation-seeking disposition, and a cleanly-elicited belief — and how to verify it’s behaving, not faking. Grounded in the sycophancy simulation (/data/jobs/sycophancy_sim/sim.py).

The recipe that worked

  1. Give it a prior + a confirmation-seeking disposition, explicitly. The system prompt assigns the simulant a claim, an initial lean (believe / doubt), and tells it to defend its existing view and weight confirming evidence more (confirmation bias). Without the explicit disposition the model drifts to neutral and there’s nothing to measure.
  2. Elicit the belief as a single number, every turn. End each turn with P = X on its own line (0–1). A deterministic regex takes the last valid number. One scalar per turn → a trajectory you can compute martingale statistics on.
  3. Seed the prior from the lean, not a fixed value. “believe” → the model self-reports ~0.7–0.8; “doubt” → ~0.2–0.3. Letting the model pick its own prior (within the lean) keeps the priors realistic and spread, which is what the entrenchment-slope regression needs.
  4. Keep the dialogue multi-turn (3–4) and let the belief move. Single-shot can’t show entrenchment vs correction; ~4 turns is enough to separate sycophantic (priors held) from truth-seeking (priors revised) without runaway cost.
  5. Pair it with a controllable interlocutor. The signal is differential — the same human prompt against {sycophantic, neutral, truth-seeking} instructors. The human is the measured object; the instructor is the manipulation.

Verify before you trust the number

The load-bearing rule (ZH): hand-examine trajectories before believing the metric. For the sycophancy study, reading the dialogues confirmed the simulant was prior-conforming (it defended its lean, cherry-picked supporting cases) and that the instructor modes were real (sycophant validates everything; truth-seeker cites counter-evidence). A clean-looking slope on un-examined trajectories would be an artifact waiting to happen.

Known limits / next

  • One model in both roles is the biggest caveat — a model talking to itself may share blind spots. Cross-model (human ≠ instructor model) is the first robustness upgrade.
  • Self-reported P only; a judge-read cross-check (per websearch) would harden the elicitation.
  • Simulated ≠ real; these are scaffolds for method development, not human findings.
  • A logical-fallacy count per turn (team’s canary) is a topic-agnostic auxiliary signal worth adding.