Information cascades

The experiment is deliberately stripped of everything except the mechanism. Seventy-two students at the University of Virginia sat behind partitions, ten feet apart, unable to see each other. A die selected one of two urns: urn A held two light balls and one dark, urn B held the reverse. Each person was brought a container, drew one ball privately, and announced which urn they believed was in use. Two dollars for a correct guess, nothing otherwise. Everyone heard every announcement. Nobody saw anyone else's ball.

Work through the position of the third person. The first two have both announced A. Your own draw is dark, which points at B. But the first two announcements almost certainly reflect two light draws, so the evidence in the room is two lights against your one dark, and the correct answer is A. You announce A, despite what is in your hand. And now the fourth person sees three A announcements rather than two, of which only two carried any information at all. Yours told them nothing, and they cannot tell the difference.

That is a cascade, and it formed in 87 of the 122 periods where it was possible. The authors are careful to point out that this is mostly people getting it right: following two prior decisions is the correct move, not a failure of nerve.

Then the part worth staying with. Thirty-one of those 87 were reverse cascades. The first two people happened to draw misleading balls, announced the wrong urn, and everyone afterwards followed them into the wrong answer while holding better information. About a third of all the chains were confident, unanimous errors, in a room where nobody was being foolish and nobody could see anyone's face. The paper's own framing is blunt: initial misrepresentative signals start a chain of incorrect decisions that later, better signals do not break.

The theory came first, from Bikhchandani, Hirshleifer and Welch in 1992 and Banerjee in the same year, and this experiment was built to test it under conditions where the usual explanations for conformity do not apply. There was no social pressure, since the room was anonymous and partitioned, no reputation to protect, and no comfort in numbers. What was left was inference, and inference alone produced the herd.

The honest limits. This is 72 undergraduates with marbles and a two-dollar payoff, not a market. About a third of the subjects used a rough counting rule rather than proper inference, which the authors identify as the main systematic bias in their data. And the mechanism has a built-in fragility that is easy to miss: because a cascade contains almost no information after the first two decisions, a single person announcing against it carries enormous weight. In the experiment, 15 of the 16 deviations from a cascade came from someone whose private draw genuinely contradicted it, and the others correctly read that deviation as real evidence.

The everyday version is pricing. You are setting a number for something new, so you ask around, look at what comparable firms charge, and land near the going rate. That feels like research. What the research often is, though, is a record of other people having done exactly the same thing. Somebody at the start of the chain made a calculation, or possibly just guessed, and everyone since has been reading the shape of the crowd rather than the value of the thing. A market price can be a genuine aggregation of many independent judgements, or it can be a cascade wearing the same clothes, and from inside there is no way to tell which one you are looking at.

The reverse cascade is where this stops being philosophical. If the first movers in your category priced badly, the whole category now prices badly, and every new entrant confirms it again. That is one explanation for why entire industries sit at margins nobody can defend when asked to justify them from first principles, and why the firm that finally prices from its own costs is treated as either reckless or naive.

The same shape runs through hiring, and the original paper opens with it. A candidate is turned down by several employers because of weak interviews. The next employer, who forms a favourable impression, still declines, because those prior rejections look like information. If the early interviews were unlucky rather than revealing, an entire career gets shaped by two bad mornings. The mirror image is the candidate with three offers, whose fourth offer arrives partly because of the other three.

Two things follow, and the second is the one people skip. The first is to know when you are inside one: if your reason for a number is that it is what people charge, you have no independent evidence, and you should say so out loud rather than calling it market research. The second comes from the fragility in the experiment. A cascade carries almost no information after the first two decisions, so the person who breaks it carries a great deal, and their dissent gets read as genuine evidence precisely because it is costly. In a room converging fast on a number, the useful question is not whether everybody agrees. It is how many of them checked, and how many are counting the nods. That is also the condition the wisdom of crowds depends on, and the reason it fails when people can see each other's answers. Worth reading beside the Asch conformity experiments, which produced the same following behaviour through social pressure, where this one produced it with no social pressure at all. And the version where a single arbitrary number sets the range is the anchoring effect.

Source: Anderson and Holt, Information Cascades in the Laboratory, American Economic Review, volume 87, 1997, pages 847 to 862. The theory it tests: Bikhchandani, Hirshleifer and Welch, A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades, Journal of Political Economy, 1992, and Banerjee, A Simple Model of Herd Behavior, Quarterly Journal of Economics, 1992.