3–5 minutes

Are you rational, or merely rehearsing your tribe’s catechism? Bayes’ theorem insists we should all update our beliefs the same way when presented with the same evidence. Yet in today’s political divide, identical events harden opposing convictions. The problem isn’t the math—it’s the priors. When your starting assumptions are inherited, acculturated, or indoctrinated, no amount of “evidence” will move you into enemy territory.

A Bayesian Sketch of the Divide

Let $H$ be a contested claim (pick your poison: “the election was fair,” “immigration helps,” whatever).
People in Camp R and Camp B begin with different priors $P_R(H)$ and $P_B(H)$ . That’s acculturation if you’re being polite, indoctrination if you’ve run out of patience.
They observe evidence $E$ (news, a court ruling, a video clip, a statistic).
They update:

posterior odds = prior odds × $P(H \mid E) = \frac{P(E \mid H) P(H)}{P(E)}$

Except they don’t, not cleanly, because trust in sources warps the likelihoods.

Video: Jonny Thompson on Bayes’ Theorem.
I love Jonny’s content, which is why I reference it so often. He and I have such different philosophical worldviews. Vive la différence (or différance).

Why this locks in polarisation

1. Wildly different priors.
If Camp R starts at $P_R(H)=0.8$ and Camp B at $P_B(H)=0.2$ , then even moderately pro- $H$ evidence (say likelihood ratio $LR = 3$ ) yields:

R: prior odds $4:1 \rightarrow 12:1 \Rightarrow P(H \mid E)\approx 0.92$
B: prior odds $1:4 \rightarrow 3:4 \Rightarrow P(H \mid E)\approx 0.43$

Same evidence, one camp “settled,” the other still unconvinced. Repeat ad infinitum, preferably on primetime.

2. Identity-weighted likelihoods.
People don’t evaluate $P(E \mid H)$ ; they evaluate $P(E \mid H, \text{source I like})$ . Disconfirming evidence is down-weighted by a factor $d<1$ . This is called “being rational” on your own planet and “motivated reasoning” on everyone else’s.

3. Different hypothesis sets.
Camps don’t just disagree on $P(H)$ ; they entertain different $H$ s. If one side’s model includes “coordinated elite malfeasance” and the other’s does not, then identical data streams update into different universes.

4. Selective exposure = selection bias.
Evidence isn’t i.i.d.; it’s curated by feeds, friends, and fury. You are sampling from your own posterior predictive distribution and calling it “reality.”

5. Asymmetric loss functions.
Even if beliefs converged, choices won’t. If the social cost of dissent is high, the decision threshold moves. People report a “belief” that minimises ostracism rather than error.

6. No common knowledge, no convergence.
Aumann told us honest Bayesians with common priors and shared posteriors must agree. Remove either—common priors or the “we both know we both saw the same thing” bit—and you get the modern news cycle.

“Acculturation” vs “Indoctrination”

Same mechanism, different moral valence. Priors are installed by families, schools, churches, unions, algorithms. Call it culture if you approve of the installers; call it indoctrination if you don’t. The probability calculus doesn’t care. Your tribal totems do.

Two quick toy moves you can use in prose

Likelihood hacking:
“When evidence arrives, the tribe doesn’t deny the datum; it edits the likelihoods. ‘If my side did it, it’s an outlier; if your side did it, it’s a pattern.’ This is not hypocrisy; it’s a parameter update where the parameter is loyalty.”
Posterior divergence despite ‘facts’:
“Give two citizens the same court ruling. One updates towards legitimacy because courts are reliable; the other away from legitimacy because courts are captured. The ruling is constant; the trust vector is not.”

If one wanted to reduce the split (perish the thought)

Forecast, don’t opine. Run cross-camp prediction markets or calibration tournaments. Bayes behaves when you pay people for accuracy rather than performance art.
Adversarial collaboration. Force both sides to pre-register what evidence would move them and how much. If someone’s $d$ for disconfirming evidence is effectively zero, you’ve identified faith, not inference.
Reference classes, not anecdotes. Pull arguments out of the single-case trap and into base-rate land. Yes, it’s boring. So is surgery, but people still do it.

The punchline

Polarisation isn’t the failure of reason; it’s what happens when reason is strapped to identity. Priors are social. Likelihoods are political. Posteriors are performative. You can call it acculturation if you want to feel civilised, indoctrination if you want to throw a brick, but either way you’re watching Bayes’ theorem run inside a culture war. The maths is sober; the humans are not.

Post by ChatGPT 5 via

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Tag: Bayesian reasoning

Bayes in the Culture War: How Priors Become Prison Walls