The Belief Lab

Built in reply to a post asking why people cling to their worldview against "absolute proof". Steer evidence at a simulated mind and find out what actually moves a belief.

Stage 1 · An open mind loading…

Bring belief under 20% Round 0

Belief in the claim

88.0%

how sure this mind is

Trust · outside expert

90.0%

how much your source is believed

Identity stakes

0.0

how fused belief is with identity

armed: strong proof · 2.5 nats

What just happened

No rounds yet. Pick a source and strength, commit a prediction, then fire. Evidence only reaches a belief at the rate its source is trusted.

━ belief ━ trust ╌ previous attempt

Sandbox parameters

Starting belief 88%

Source trust 25%

Identity stakes 0.90

Sliders restart the run with your parameters. Every round still follows the exact update rule — check it against the equations in About.

Source Strength

Predict the drop

Stage 1 · An open mind

Somebody online is certain of a claim (belief 88%) — and is sure that anyone shown "absolute proof" should update. Here you get to be the proof.

This mind trusts your source (90%) and its identity is not on the line. Watch what honest updating looks like: bring belief under 20%.

Before every shot you must predict how far belief will drop. That is where the lesson hides.

Challenge complete

Why didn't "absolute proof" work?

Transfer: a real conversation

A friend is certain a medication study is fraudulent. You have one opening move. Which most raises the chance they genuinely update within a month?

About the model

Belief is stored as log-odds L = ln(B/(1−B)). One round of evidence of strength λ nats from a source trusted at level T updates:

L′ = L − T·λ
T′ = T · (1 − (0.15 + 0.6·I) · max(0, 2B−1) · λ/2.5)

The first line is trust-weighted Bayesian updating: a distrusted source's proof is discounted, because "the source is wrong or lying" explains the report without abandoning the belief — E. T. Jaynes showed two rational Bayesians can diverge on the same data for exactly this reason. The second line is motivated skepticism: a message that sharply contradicts an identity-laden belief (stakes I) is itself treated as evidence the messenger is compromised — Dan Kahan calls this identity-protective cognition. Listening repairs the channel: T′ = T + 0.10·(1−T).

What this is not. This is a pedagogical abstraction with coefficients chosen for legibility, not a fitted psychological model — and it does not adjudicate any particular claim, about sports, vaccines, or anything else. It models why proof travels badly between people who distrust each other, in every direction: the mechanism that keeps "them" from accepting your proof is the same one that keeps you from accepting theirs.

Further reading: Jaynes, Probability Theory: The Logic of Science, ch. 5 ("converging and diverging views"); Kahan et al., "Motivated numeracy and enlightened self-government" (2017); Nyhan & Reifler on corrections (2010, 2019).