Bikhchandani, Hirshleifer & Welch, 1992 — how a group of perfectly rational people goes wrong in unison
Why do fashions arrive in a block and leave in a block? A queue forms outside a newly opened restaurant, and the overwhelming majority of the people in it have no idea whether the food is good — they saw a queue. A stock, a parenting doctrine, a programming framework: each can be adopted by everybody in a short window and then abandoned by everybody without a single new piece of evidence arriving.
The older explanation is conformity: people need to belong and fear standing out. The trouble with that explanation is that it predicts nothing. It cannot say when conformity will happen and when it won't, and it cannot say why a monolithic trend can flip overnight.
This model asks a sharper question: if everyone were perfectly rational, cared only about being right, and were entirely indifferent to what others thought of them, would the same thing still happen? It would. And it would happen faster than conformity predicts.
Note what is absent: no taste for conformity, no social pressure, no authority, nobody stupid, nobody lying. Every person's objective function has exactly one term — be right.
The standard physical version is the urn experiment: urn A holds 2 red balls and 1 blue, urn B holds 2 blue and 1 red; the experimenter picks one urn at random, each participant privately draws a ball, looks, replaces it, then publicly announces which urn they think it is. Here q = 2/3.
The decisive step happens at the third person, and only three steps are needed.
Run the process a few more times and three things show up.
One: cascades start very fast, and they often start wrong. With the urn setting q = 2/3, the moment the first two signals agree the cascade is locked — and the chance of two signals both pointing the wrong way is not small. The standard Bayesian calculation puts the probability of ending in a wrong cascade at (1−q)²/(1−2q+2q²), which at q = 2/3 is about 1/5. One time in five, an entire population settles into being wrong, stably, indefinitely. And that probability does not fall with group size: bring in ten thousand people and it stays 1/5, because from the third person onward nobody adds any information.
Two: they are brittle. Since nobody downstream carries information, one genuinely new piece of public evidence can flip the whole queue on the spot. This is why fashions leave even more abruptly than they arrive, and why "everyone's doing it" collapses so completely once it is punctured — there was never anything underneath.
Three: better signals lock the cascade sooner. Raise q, so every individual's signal is more accurate, and cascades form earlier — because the first two public decisions now carry more weight and more easily override later private signals. This is the most counterintuitive result of the lot: improving the judgment of each individual does not necessarily improve the judgment of the group.
Anderson and Holt took this setup into the laboratory in 1997 with real people and real money. The fit to theory was good: cascades formed frequently, including incorrect ones, and in the great majority of rounds participants' behaviour matched the Bayesian prediction — they were not following blindly, they were calculating.
Why queues reinforce themselves. The line outside a restaurant is a sequence of public decisions. The first few people may genuinely have done their homework; everyone after them saw a line. So "popular" is a mixture: partly quality, partly the luck of the first two or three — and from outside the proportions are invisible.
Why trends are simultaneously sticky and fragile. The adoption curve has an abnormally steep early jump (the moment of locking), then a rock-solid middle, and then can collapse entirely after a single news item. Explaining all three phases at once is hard with conformity; with cascades it falls out naturally.
Why expert communities also go wrong together. Nothing in the model requires participants to be unqualified. Take the same high-calibre people, have them speak in sequence with each other's conclusions visible, and cascades form all the same — locking earlier, in fact, when q is higher. Academic consensus, clinical guidelines and sell-side research all have this structure.
It identifies exactly where to intervene. The model has only three movable parts: order (who speaks first), visibility (whether others' decisions can be seen), and whether what gets published is the decision or the signal. The third is the most powerful — if people publish not only their conclusion but the evidence behind it, private signals enter the public pool and cascades cannot form at all. That is the model-level justification for "publish reasons, not vote counts."