Sycophant vs. Devil's Advocate

A single addition to Zollman's bandit-network model. Each scientist holds a credence that the new theory is the better one, updated on evidence like coin-flips. A private consultation adds c imaginary observations that carry no real data. A sycophant ("you're right") makes them match your current credence — believe 70%? it hands you ~0.7c confirmations and ~0.3c doubts: the number stays put but grows more confident and harder to shift (reinforcement as pure stubbornness). A devil's advocate ("you're wrong") flips the split (~0.3c / ~0.7c), dragging your credence toward the rival theory. "Deference" (the slider) is how large c is. Old theory pays 0.5, the new one 0.5 + ε — who finds out, and does the LLM help or hurt?  ·  ← tutorial

Zollman's model

who sees whose results. Zollman's headline: sparser networks are slower but likelier to find the truth
how much evidence each working scientist generates each round — the yardstick the LLM's word is measured against
Zollman's "extreme beliefs": how much contrary evidence it takes to move a scientist off its starting opinion (the stubbornness they start with). Cranked to the top on the cycle, it reproduces Zollman's sparse-network collapse — everyone stays put and the community never settles; on the complete graph the same extremity instead rescues it.

The LLM (private)

each scientist consults a private model about their own current view. Sycophant = a stubbornness dial; devil's advocate = an exploration dial

Simulation

independent communities to simulate — more runs, steadier percentages (heavier compute: the panels sweep many conditions)
Panels update automatically as you change anything; "Recompute" just reruns at the current settings (e.g. after a new seed).
Log sliders: ε = 10−3+x, trials = 10x, prior = 10x, deference = pseudo-observations = 10x. Everything runs client-side; nothing leaves this page.
Press Run.

The community (topology + each scientist's private LLM)

Effect on this community (outcome probabilities here)

Which network are we in? (P settle on truth vs. never-settle, across networks)

Dose–response on this network (vs. deference)

Sample trajectories (fraction on the new theory; the selected LLM)

What "deference" is, exactly. Each scientist holds a Beta(α, β) belief with credence e = α/(α+β). A consultation does α += c·v, β += c·(1−v), with v = e for the sycophant — mean-preserving, so e is unchanged while the total mass α+β grows (more confidence, no new information) — and v = 1−e for the devil's advocate, which shifts e toward the rival theory. The LLM adds no evidence; c (deference) is how many pseudo-observations its reply is worth. At 0 it is ignored; when c approaches a round of your own work (trials) it starts to rival real data.
Private only, for now. Here each scientist consults a model that mirrors their own view. The shared model — one foundation model everyone consults, reflecting the community's consensus — is held in reserve: it behaves differently (it adds a covert edge between every pair of scientists, densifying the network), and a shared sycophant is harmful across the board. That's the sequel.
The result to watch. The devil's advocate is the network-robust choice: it helps dense communities and does not wreck sparse ones. The sycophant is a stubbornness dial — a targeted tonic for over-connected communities that overshoots into permanent diversity (the grey "never settles" bar) on sparse ones. If you don't know which network you're in, challenge dominates.