TL;DR
The formal argument for trusting majorities — Condorcet’s jury theorem — requires two conditions: each person must be right more often than chance, and their judgements must be independent. Drop independence, and the probability of a correct majority converges to something strictly below certainty.1 Experimentally, mild social influence is enough: in a study of 144 subjects, letting people see others’ answers narrowed the spread of estimates without reducing collective error, while boosting confidence.2 Worse, following the crowd is often individually rational — in laboratory cascade experiments, herds formed in 87 of 122 opportunities, and roughly a third of them converged on the wrong answer.3 And sometimes the consensus is held by nobody: students in four studies each believed they were more uncomfortable with campus drinking than the average student was.4 Agreement is a fact about a group’s wiring, not about the world.
A starling murmuration. No bird can see the flock; each is tracking a handful of neighbours, and the density is what that produces. Photo: Skander zarrad, CC BY-SA 4.0.5
The Line That Sounds Like Crankery
“Consensus isn’t correctness” is the favourite sentence of people who are wrong. It arrives in defence of flat earths and miracle cures and every position that has lost an argument on the merits, deployed as a general solvent: they all agree, and they’ve all been wrong before.
So it’s worth separating the sentence from the people who abuse it, because as stated it is simply true, and the interesting question is the one the crank never asks. Not is consensus proof? — obviously not — but under what conditions does agreement carry evidential weight, and how do you tell whether those conditions held?
That question has an answer. It’s older than the abuse, and it’s more demanding than most people who invoke consensus realise.
The Condition Attached to the Theorem
The formal case for majority rule as a truth-tracking device is Condorcet’s jury theorem, and it is genuinely powerful. If each member of a group has an equal, better-than-random but worse-than-perfect chance of judging correctly, and if their judgements are stochastically independent given the state of the world, then the majority is more reliable than any individual member — and the probability of a correct majority judgement approaches 1 as the group grows.1
That is a remarkable result. A hundred people each 55% likely to be right, voting independently, will collectively be right almost always. It is the mathematical backbone of a great deal of confidence in juries, elections, markets and peer review.
Note the second clause. Independence is not decorative; it is load-bearing. And the Stanford Encyclopedia entry is direct about what happens without it: whether independence holds depends on the decision problem, and if voters’ judgements become correlated — particularly if they “mimic a small number of opinion leaders” — the probability of a correct majority decision converges at most to a number strictly below 1.1
So the theorem does not say large groups are reliable. It says large groups of independent judges are reliable. The gap between those two sentences is where almost every real consensus lives.
How Little Influence It Takes
The natural response is that a bit of correlation surely can’t matter much. People talk, they read the same things, they hear a few opinions before forming their own — and the crowd is still large. Surely the effect is marginal.
It isn’t, and the demonstration is clean. Jan Lorenz and colleagues ran an experiment with 144 subjects answering factual estimation questions across five consecutive periods, comparing a control condition with conditions where subjects saw either the average of others’ answers or the full set before revising.2
Their conclusion is that even mild social influence undermines the wisdom-of-crowds effect, and they decompose it into three named effects.2 The social influence effect: knowledge of others’ estimates diminishes the diversity of the crowd, without improving its collective error. The range reduction effect: as the estimates converge, the true value ends up in the peripheral regions of the range rather than the middle — so an outside observer reading the crowd’s spread gets a worse signal than before. And the confidence effect: after converging, individuals are more confident, despite no improvement in accuracy.2
Read the third one slowly, because it’s the mechanism by which this becomes invisible. The group’s subjective sense that it has converged on the truth rises exactly when its objective claim to have done so does not. Confidence tracks agreement, and agreement here is a product of exposure, not of evidence.
The Uncomfortable Part: It’s Rational
The easy story is that people conform out of weakness — social pressure, cowardice, laziness. That story is comforting because it implies the fix is character.
The cascade literature removes that comfort. Lisa Anderson and Charles Holt built a laboratory setup deliberately stripped of social pressure: subjects privately drew a ball from an unseen urn, then publicly guessed which of two urns it came from, in sequence, paid only for being correct.3 No reputational stake in agreeing. No one watching disapprovingly.
The logic is straightforward. If the first two people both announce urn A, the third person — who drew a ball suggesting B — can infer that two private signals pointed to A and only one to B. Following the crowd is the correct Bayesian move. But the moment they do it, their own signal vanishes from the public record. Everyone after them sees the same imbalance and reasons the same way. The information stops accumulating while the agreement keeps growing.
The results: cascades formed in 87 of the 122 periods in which they were possible, and the authors note that individuals generally used information efficiently and followed others when it was rational to do so.3 But of those 87 cascades, 31 were “reverse” cascades — the early draws happened to be misleading, and the whole chain locked onto the wrong urn, with later subjects abandoning correct private signals to join it.3 Roughly one in three consensuses in a clean, incentive-aligned, no-pressure laboratory was simply wrong, and stayed wrong.
That is the finding worth carrying around. The unanimity is not produced by people being irrational. It is produced by people being sensibly deferential in a sequence — which is to say, by exactly the behaviour we would recommend to them.
Consensus Nobody Actually Holds
There is a stranger failure mode, in which the majority position is one that the majority privately rejects.
Deborah Prentice and Dale Miller ran four studies on students’ attitudes toward campus alcohol use and their estimates of their peers’ attitudes.4 Across all of them: students believed they were more uncomfortable with campus alcohol practices than the average student was.4 Everyone privately dissenting, everyone publicly assuming they were the outlier.
The follow-through is the important part. Tracking attitudes over a semester, male students shifted their views over time toward what they mistakenly believed the norm to be; female students showed no such change.4 And a fourth study found students’ perceived deviance correlated with measures of campus alienation — even though the deviance was illusory.4 People adjusted their real beliefs, and paid a real social cost, to match a consensus that did not exist.
So the count of a public consensus can be untethered from the count of private beliefs in both directions: people can converge on a view none of them independently reached, and they can feel isolated by a majority that isn’t there.
What This Does Not License
Now the part that separates this argument from its most enthusiastic users, because everything above can be turned into a licence for nonsense if you let it.
None of this establishes that consensus is uninformative. It establishes that consensus is informative in proportion to the independence of the judgements composing it, and that independence is fragile and rarely audited. Those are different claims, and the second one cuts both ways.
Which means the practical test is not “do lots of people believe it?” but “how did they come to?” A conclusion reached by many groups, using different methods, in different countries, some of whom were actively trying to disprove it, is a very different object from a conclusion reached by many people who read the same three sources. The first approximates the theorem’s conditions. The second is a cascade with a large sample size.
This is, incidentally, why the machinery of science looks so pedantic from outside. Independent replication, blinded review, pre-registration and adversarial collaboration are all, structurally, devices for manufacturing the independence that Condorcet’s theorem requires and that ordinary social life destroys. They exist because agreement produced by people watching each other is known to be worthless, and the field went to considerable trouble to produce agreement of a different kind. Whether that machinery works as advertised is a separate question, and a live one — but the design intent is exactly the condition identified here.
And the symmetric point, which the crank always skips: “the consensus formed through a cascade” is itself an empirical claim requiring evidence. You do not get to infer it from the mere fact that people agree, any more than they get to infer truth from it. If you cannot say how the agreement formed, you know nothing either way — you have simply moved your unjustified confidence one level up.
Where I’d Hold This Loosely
Two limits worth stating.
The laboratory results are laboratory results. Estimation tasks with numeric answers and urn-drawing games are chosen precisely because the truth is knowable and the information structure is controllable, which is what makes them informative and also what makes extrapolation to messy public disagreements a stretch. The cascade mechanism is well specified; how much of any given real-world consensus it explains is not something these experiments can tell you.
Second, the Lorenz findings have been contested in print — a published exchange in the same journal disputed whether social influence harms the individuals in the crowd, with the original authors replying that improved individual estimates can coexist with collective tunnel vision. I could not access that correspondence, so I’ll note its existence rather than characterise it further, and treat the strong version of the claim as somewhat less settled than the experiment alone suggests.
What survives is modest and, I think, usable. Agreement is a measurement of a social process. Whether it is also a measurement of the world depends entirely on whether the people agreeing were in a position to disagree — and on most questions, by the time you hear about the consensus, they no longer were.
