Sycophant vs. Devil's Advocate

One addition to Zollman's model, on the faithful engine (both theories' success rates unknown; every scientist holds a belief about each and works on the one that currently looks better). Each scientist now also has a private interlocutor that has run no trials but talks as if it had: its reply is received as c pseudo-trials (the deference slider). A sycophant hands back the scientist's own belief about the theory in hand — the estimate stays put, it just gets heavier and harder to move. A devil's advocate says "the grass is greener": the theory in hand is no better than the other, and the other no worse than this one — pulling the two estimates toward each other, and pushing toward switching. The new theory pays 0.5, the old one 0.5 − ε. Who finds out, and does the interlocutor help or hurt?  ·  ← tutorial  ·  the original model →

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 interlocutor's word is measured against
Zollman's "extreme beliefs" (max α/β = 4 × strength): the stubbornness scientists start with. The sycophant manufactures the same thing on the fly.
untick to replay the EARLIER BUILD: the old theory's rate is known, giving the new theory up is permanent, the sycophant echoes everyone's belief about the new theory whatever they are working on, and the devil's advocate flips that belief about 0.5. Its findings (challenge is network-robust, sycophancy deadlocks sparse networks) live there.

The interlocutor (private)

each scientist consults a private model before every decision, including the first. Sycophant = a stubbornness dial; devil's advocate = an exploration dial

Simulation

independent communities per condition — more runs, steadier percentages (the network and dose panels run 24 conditions each)
when the verdict is read. The sycophant's harm on sparse networks is a delay, so it shrinks as this grows — try 2,000 and 10,000
Panels recompute when you change anything, top to bottom; the heavy ones fill in as they finish.
Log sliders: ε = 10−3+x, trials = 10x, prior = 10x, deference = pseudo-trials = 10x. Everything runs client-side; nothing leaves this page.
Computing…

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

Effect on this community (outcomes at the horizon: none / sycophant / devil's advocate at this deference)

Grey is the share still divided when the verdict is read. In this engine a community on the wrong theory is not doomed in principle, and a divided one is not stuck: grey means "not yet", and shrinks with the horizon.

Which network are we in? (P settle on the truth, across networks, at this deference)

Dashed tick: no interlocutor. Grey cap on a bar: still divided at the horizon.

Dose–response on this network (vs. deference)

Solid: P(settle on the truth). Dashed: still divided at the horizon.

Diversity trajectories (average share of scientists on the new theory, grouped by how the community ends up; the selected interlocutor)

When is the question settled? (share of communities at their final verdict, by round; the selected interlocutor)

This is where the sycophant's cost on a sparse network shows first: the blue curve climbs later. Log axis.

What "deference" is, exactly. Each scientist holds a Beta(α, β) belief about each theory, with estimate E = α/(α+β). Let H be the theory that currently looks better to them and O the other. A consultation adds c pseudo-trials. Sycophant: H's belief gets c trials at EH (αH += c·EH, βH += c·(1−EH)) — mean-preserving, so the estimate is unchanged while its weight grows; O is untouched (the variant touches both). Devil's advocate: H's belief gets c trials at EO and O's belief gets c trials at EH — each estimate is pulled toward the other's, so the push is exactly as large as the gap the scientist perceives, and vanishes as the two estimates converge. Neither adds evidence; c is how many observations the reply is worth. When c approaches a round of your own work (trials) it rivals real data.
Why the sycophant is Zollman's Assumption 5 in disguise. At the first consultation a weightless prior (mass ≈ 4) receives c pseudo-trials at its own mean: that is his "extreme belief" with maximum α/β ≈ c, and his Figure 6 says extreme beliefs rescue the dense network and slow the sparse one. Thereafter the weight is topped up every round, so unlike a one-time prior it is never swamped: the scientist's learning rate is permanently scaled by real trials ÷ (real trials + c).
Why the devil's advocate touches the belief his Assumption 3 freezes. A scientist on A generates no evidence about B, so their belief about B is frozen. The devil's advocate is the one voice that keeps moving it — a stand-in for the exploratory experiment a myopic scientist refuses to run.
Private only, for now. A shared model that everyone consults, reflecting the community's consensus, is a different object (a covert edge between every pair of scientists) and is not on this page.