Traveler herding

Why do travellers crowd into the same few places while equally good ones stay empty?

Two valleys sit an hour apart. Comparable scenery, comparable walks, comparable food. One receives four hundred thousand visitors a year and the other four thousand. Ask anyone in the crowded valley why they came and you will get a confident answer — and almost none of those answers will be "I compared the two."

The tempting explanation is that the crowd knows something. Sometimes it does. But notice how strange the arithmetic is: if the crowd's judgement were the sum of four hundred thousand independent assessments, it would be formidable evidence. Is that what it is?

Suppose you are choosing between the two valleys. You have a private signal — a photograph you liked, a friend's remark, a paragraph in a book — and it is weak. It leans, faintly, toward the quiet valley. But you can also see what others chose, because their choices are public: booking counts, review volume, the queue at the trailhead.

Take the travellers in order. The first has nothing to observe, so she follows her own signal and picks the busy valley. The second sees one choice for the busy valley and holds a private signal for the quiet one. Evidence for and against, roughly balanced, and he tips either way.

Now the third. She sees two choices for the busy valley and holds one weak signal against it. What should a perfectly rational person do? Follow the two, and abandon her own signal — because two pieces of evidence outweigh one. This is not a failure of reasoning. It is reasoning working correctly.

Here is the turn, and it is the whole thing. Because she abandoned her signal, her choice reveals nothing about what she knew. The fourth traveller sees three choices for the busy valley, but only two of them ever carried information. The fifth sees four, still carrying two. The pool of evidence stopped growing at the moment people started copying, and everyone after that is inferring from a tally that has been frozen since the beginning.

This is what Bikhchandani, Hirshleifer and Welch called an information cascade, in 1992. Their point was sharper than "people imitate". It was that imitation can be individually rational and collectively disastrous — the crowd converges on an option that perhaps two people ever independently judged, and every subsequent traveller is entitled to believe the crowd knows more than it does.

Ask what follows. First, the outcome is arbitrary: run the same population again in a different order and the cascade can land on the other valley just as easily. Second, and this is the property worth holding onto, the cascade is fragile. It rests on almost no real information, so it takes almost no real information to break it. One credible public fact — a broadcaster's report, a well-read guide naming the quiet valley — can outweigh a tally of thousands, because the thousands were only ever worth two. Cascades shatter far more abruptly than accumulated evidence ever would.

Two refinements connect the steps. The first: the crowd is not evidence of nothing. It reliably encodes the first few private signals, and those may well have been right. The claim is about weight, not truth — a hundred thousand visitors is not a hundred thousand endorsements, and treating it as one is the error.

The second: crowding usually makes a place worse. A queued viewpoint is a poorer viewpoint. So why does the negative feedback not correct the imbalance? Partly because the crowd is read as a quality signal at the moment of choosing and only experienced as congestion after arriving, by which point the choice is already in the public tally. The two effects fight, and which wins depends on how visible the congestion is beforehand.

The honest limits. Cascades are one mechanism among several, and real concentration also has plain physical causes — one valley has the airport, the road, the hotel stock, the visa-free border crossing, the film location. Those alone would produce imbalance without any inference at all. And while cascade behaviour is well demonstrated in laboratory experiments, separating it from ordinary advertising and infrastructure in field data is genuinely hard. Take the mechanism as a real contributor whose share is contested, not as the explanation.

• Why ranking algorithms and review counts sharpen cascades rather than correcting them.
• How the same mechanism explains fashion cycles, bank runs, and academic citation patterns.

Every term the collection defines is gathered in the glossary.