Agents arrive one at a time, each drawing a private noisy signal about which of two restaurants is actually better, then choosing publicly after seeing everyone who went before them. Watch a herd form — and see whether it lands on the right answer.
The Bikhchandani-Hirshleifer-Welch information cascade: once the public tally of prior choices leans two or more toward one option, that imputed "vote" outweighs any single private signal, so later agents rationally stop using their own information and herd — even if the herd is wrong.
Click Step to add one agent at a time, or Play to auto-run the sequence. Watch the timeline: a red dashed ring marks an agent who ignored their own signal to herd. Toggle Reveal to check the hidden true state and each private signal, then Reshuffle for a fresh run.
Because a cascade can start from just two early, possibly coincidental, matching choices, it can lock the whole crowd onto the wrong option forever — no later agent's private information ever gets revealed or aggregated once herding begins.
This simulation models the classic sequential-decision setting formalised by Sushil Bikhchandani, David Hirshleifer and Ivo Welch in their 1992 paper "A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades" (Journal of Political Economy). A hidden true state — here, which of two restaurants is actually better — is never directly observed. Agents arrive one at a time, each drawing a private, noisy signal correlated with the truth, and each observing the full public history of choices (but not the private signals) made by everyone before them. A rational agent combines their own evidence with the informational content implied by the crowd's prior choices.
The striking result is that once the public tally of choices leans strongly enough toward one option, that "imputed vote" can outweigh a single private signal, so it becomes individually rational to ignore your own evidence and copy the crowd — a cascade. Because the cascade can be triggered by nothing more than two early, possibly coincidental, agreeing signals, an entire population can herd onto the wrong option, and no later agent's information ever surfaces to correct it. The model explains real phenomena from stock-market bubbles and bank runs to restaurant popularity, IPO underpricing and the adoption of new technologies or medical treatments.
An information cascade occurs when individuals making a sequence of decisions rationally choose to ignore their own private information and instead copy the choices of those who acted before them. It happens because each person's choice reveals a little information to everyone watching, and once enough choices point the same way, that public signal becomes more informative than any single person's private evidence — so imitation, not independent judgment, drives the outcome.
Click "Step" to bring in one agent at a time, or "Play" to auto-run the sequence at the chosen speed. Each agent appears as a colored circle in the timeline: violet for choice A, amber for choice B, with a small dot showing their private signal (hidden until you click "Reveal"). A red dashed ring means that agent ignored their own signal to herd. Use "Reshuffle" to randomise the hidden true state and start over.
Herding is when an agent's public choice contradicts their own private signal because the accumulated weight of prior public choices outweighs it. In this simulation that happens once the running tally of choices differs by two or more in one direction: from that point on, every subsequent agent's optimal strategy is to copy the majority regardless of what their own private signal says, which is exactly what the red dashed rings highlight.
Economists Sushil Bikhchandani, David Hirshleifer and Ivo Welch formalised the model in their 1992 paper "A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades," published in the Journal of Political Economy. A closely related model was independently developed the same year by Abhijit Banerjee. Together these papers launched a large literature on sequential social learning, herd behaviour, and the fragility of decisions built on borrowed rather than original information.
Yes — that is the central, counterintuitive result of the model. A cascade can start after only two agents happen to receive matching private signals, even if those signals are individually noisy and even if the majority of the population would, if consulted independently, have leaned the other way. Once locked in, the cascade is self-reinforcing: no later agent's private information is ever revealed to the public, so an incorrect cascade has no built-in mechanism to self-correct.
Signal accuracy p is the probability that a private signal matches the true state. Higher p makes each individual signal more reliable, so the very first agents — whose choices seed the eventual cascade — are more likely to reveal the true state before herding begins. This does not prevent cascades from forming (the ±2 threshold rule is the same either way), but it substantially raises the probability that, when a cascade does form, it locks onto the correct option rather than the wrong one.
Real-world cascades are known to be fragile: a small amount of new public information — a bad review going viral, a credible outsider revealing a contrary signal, or a policy announcement — can break an established cascade and trigger a rapid reversal, since agents were never actually convinced, merely imitating. This "informational fragility" is used to explain sudden crashes in fads, financial markets and bank runs, which can look stable for long periods and then unravel abruptly once contradicting information becomes public.
The model has been applied to explain restaurant and product popularity despite similar quality, IPO underpricing and stock market bubbles, bank runs and financial contagion, the rapid adoption or rejection of medical treatments and new technologies, jury and voting behaviour, and fashion and cultural fads. In every case, the common thread is that people observe each other's choices more easily than they observe each other's private information.