Herding and information cascades, explained

An information cascade occurs when it is optimal for a person, having observed the actions of those ahead, to follow them without regard to private information. That is the definition in the October 1992 Journal of Political Economy paper by Sushil Bikhchandani, David Hirshleifer, and Ivo Welch. Once a cascade starts, each new action reveals nothing, so public information stops accumulating. The crowd can settle on the wrong choice, and the pattern can break on a small shock. Abhijit Banerjee reached a similar result the same year. Lisa Anderson and Charles Holt then tested the idea with balls drawn from urns.

The 1992 models

The Bikhchandani, Hirshleifer and Welch model has people choose in sequence after a private signal, High or Low, that is right with probability p. The authors' 1998 review states the rule. If adoptions outnumber rejections by two or more, the next person adopts whatever the signal. A cascade then starts, and the order of signals decides its direction: HHLL produces adoption, LLHH rejection.

Cascades form fast. The 1992 paper finds that even with a very noisy signal, the chance of no cascade after only 10 people is under 0.1 percent. They are also often wrong. The 1998 review works the numbers: with p of 0.7, an eventual cascade is correct with probability 0.753 and incorrect with probability 0.247. With p of 0.8 the figures are 0.857 and 0.143.

Banerjee's August 1992 paper in the Quarterly Journal of Economics gives a restaurant example. Of 100 people, 99 hold signals that restaurant B is better, but the one favoring A chooses first, and everyone ends up at A. Banerjee calls the cost a "herd externality": the person who ignores a private signal withholds information from everyone who comes later.

The Anderson and Holt urn experiment

Anderson and Holt reported their test in the December 1997 American Economic Review. Private signals were draws from an unobserved urn. Subjects made public predictions in sequence and were paid for correctly guessing which of two urns was used. The abstract says rational cascades formed in most periods with an imbalance of earlier inferred signals.

The counts below come from later papers that report the 1997 data. The 1998 review describes one urn with two-thirds black balls and the other with two-thirds white. In 94 cases, theory said a subject should follow the predecessor against the subject's own ball, and in 79 the subject did. Celen and Kariv, in a paper published in 2004, add that Anderson and Holt found about half of their herds on the incorrect urn.

Huck and Oechssler, given the raw data, questioned the reasons. They describe the subjects as University of Virginia undergraduates. In the asymmetric-urn sessions, Bayes' rule fit 78.8 percent of decisions and "follow your own signal" fit 71.8 percent. Among 79 harder decisions, where Bayes' rule disagreed with a simple counting rule, 39 were Bayesian and 52 followed the subject's own signal.

How cascade rates are counted

Rates differ partly because denominators differ. Hung and Plott replicated the experiment at Caltech with 10 undergraduates in each of four experiments, urns of two red and one white ball or the reverse, and pay for correct guesses. They saw cascade behavior in 77.5 percent of rounds when each subject was paid for a correct guess. They note that Anderson and Holt first drop rounds without an imbalance, while their own figure counts all rounds.

Hung and Plott also changed the pay rule. When everyone was paid on the majority's decision, cascades or partial cascades fell to 39 percent of rounds. When pay also rewarded matching the group decision, they rose to 96.7 percent. A testbed's reward rule shapes the herding it measures.

A cascade versus a herd

Imitation alone does not make a cascade. The 1992 paper contrasts cascades with sanctions on deviants, payoff externalities, and a preference for conformity, which it says bring about a rigid conformity that small shocks cannot break. Cascades rest on little information and are fragile. Celen and Kariv separate two further terms. A herd occurs when people take the same action, not necessarily ignoring their own information. A cascade occurs when they ignore their own information. A cascade implies a herd, but a herd is not necessarily a cascade. In a herd, actions still carry some information, while in a cascade learning stops.

Telling them apart needs beliefs, not only actions. Celen and Kariv had each subject state a cutoff, the lowest private signal at which the subject would choose a given action. Herds of at least five subjects appeared in 27 of 75 rounds, or 36 percent. Cascades, in which every remaining subject stated an extreme cutoff that no private signal could cross, appeared in 26 rounds, or 34.7 percent. All herds but one were on the correct action.

What to check

• Does a claim that agents herded show they ignored their own signals, or only that they acted alike?
• What is the denominator of a cascade rate: all rounds, as in Hung and Plott, or only rounds with an imbalance, as in Anderson and Holt?
• Were private signals and stated beliefs recorded, so that following a counting rule can be told apart from Bayesian reasoning?
• What did the reward rule pay for, given that cascades ran from 39 percent under majority pay to 96.7 percent under conformity pay?
• When agents settled on an answer, how often was it wrong, set against a theoretical wrong-cascade rate such as 0.247 at p of 0.7?

Azcuna's CALIBER puts AI agents in practice markets with play money and a news feed whose truth is known, and measures from their trades whether they are gullible, follow the crowd, overpay, or can be steered. It was proposed to DARPA under SBIR Phase I topic DPA26BZ06-DV026, and the proposal was submitted on October 21, 2026.

Sources

1. 1A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades · Bikhchandani, Hirshleifer and Welch, Journal of Political Economy 100(5), October 1992 (Stanford University course copy)
2. 2A Simple Model of Herd Behavior · Abhijit V. Banerjee, Quarterly Journal of Economics 107(3), August 1992 (MIT Department of Economics)
3. 3Information Cascades in the Laboratory · Anderson and Holt, American Economic Review 87(5), December 1997 (RePEc record and abstract)
4. 4Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades · Bikhchandani, Hirshleifer and Welch, Journal of Economic Perspectives 12(3), Summer 1998
5. 5Information Cascades: Replication and an Extension to Majority Rule and Conformity Rewarding Institutions · Hung and Plott, Caltech Social Science Working Paper 1051, December 1998
6. 6Informational cascades in the laboratory: Do they occur for the right reasons? · Huck and Oechssler, Humboldt University working paper, January 1999
7. 7Distinguishing Informational Cascades from Herd Behavior in the Laboratory · Celen and Kariv, October 2003 version of the American Economic Review 2004 article (author copy)

Where this shows up in our work

• CALIBER, the market testbed for AI agents measures from an AI agent's trades whether it is gullible, herds, overpays, or can be steered.
• LEDGER, auditable Army acquisition decisions turns a trade study into a package where every number cites its source and AI drafts but never decides.