When Copying Is the Rational Move

Answer to the question

When is herd behaviour the rational move?

Copying is the rational move when people chose in sequence, their choices are visible, those choices were made independently on evidence, and their situation resembles yours. The first three are usually checkable. Independence rarely is, and it is the condition that decides whether herd behaviour is a sound inference or an expensive habit.

Key takeaways

• Banerjee and, independently, Bikhchandani and colleagues showed in 1992 that optimising individuals end up copying rather than using their own information, and that the resulting equilibrium is inefficient.
• In a randomised restaurant field experiment, a plaque listing the five most popular dishes raised demand for them by 13 to 20 per cent, with no significant saliency effect, and dining satisfaction rose as well.
• A randomised experiment on a news aggregator found that a fabricated first up-vote inflated final scores while a fabricated down-vote was corrected away, which pure information-weighting does not predict.
• The 92 per cent trust figure the trade quotes comes from a 2011 Nielsen online-only panel and measures stated trust in a channel, mostly recommendations from people the respondent already knows.
• No full text was obtained for any of the twelve journal articles cited here, and the article says so where a reader would assume otherwise.

The question asked about herd behaviour is always whether you had the nerve to think for yourself. That is the wrong question, because the copier is usually reasoning correctly. The better one: was the crowd's information worth anything?

Banerjee's answer: copying is rational

Abhijit Banerjee published the formal answer in 1992. His model is sequential: each person looks at what the people ahead of him chose, and copying is rational because those people may hold information he does not. Three sentences of his abstract carry the case.

> "We analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision. This is rational for her because these other decision makers may have some information that is important for her ... people will be doing what others are doing rather than using their information ... the resulting equilibrium is inefficient."

Read those as three claims rather than one. Copying is rational for the individual. Copying is what optimising individuals do. The outcome is inefficient anyway. Nobody in that model is insecure, weak-willed or socially anxious, and the crowd still ends up worse off than the information inside it should allow. An economist stated the inversion thirty-four years ago.

Nobody in that model is insecure, weak-willed or socially anxious, and the crowd still ends up worse off than the information inside it should allow.

Sushil Bikhchandani, with David Hirshleifer and Ivo Welch, arrived at the same place independently that year and gave it the name that stuck. An informational cascade is the state in which somebody who has watched the choices ahead of him finds it optimal to follow them whatever his own signal says. Once he copies, his choice tells the next person nothing about what he knew. Their second result is the one worth keeping: a crowd built that way is fragile, resting on very few signals, so a small amount of contrary public evidence can flip it. They concede the model cannot say when the flip arrives.

One declaration, because the paragraphs above read like the work of people with the papers open. This piece draws on twelve journal articles and we obtained the full text of none of them. We read abstracts, publisher records and, in two cases, nothing past the bibliographic entry. Where a deposited abstract stops short of the results, the prose below says so. Where claims about group intelligence rest on weak footing, an article asking [whether collective intelligence is real](https://thewhyweproject.com/articles/is-collective-intelligence-real) says how much holds.

The cascade literature's four conditions

Rationality in those models is not a general licence. The result needs four things, each an empirical question rather than a fact about the world.

1. People choose in sequence, and later choosers can see earlier choices.
2. Choices are observable and reasons are not. You see that they went in. You never see why.
3. The early choices were made independently, on evidence somebody actually gathered.
4. Their situation resembles yours closely enough that a good choice for them is a good choice for you.

Three of them are usually visible from where you stand.

The third almost never is, and the third decides whether herd behaviour is a sound inference or an expensive habit.

Lisa Anderson, with Charles Holt, put the structure into a laboratory in 1997. Private signals were draws from an unobserved urn, subjects announced predictions in sequence, and they were paid for guessing right, so following the crowd carried a price. Rational cascades formed in most periods in which an early imbalance appeared. Angela Hung and Charles Plott later published a replication extending the design to institutions that reward conformity, and we have its title and status and nothing further.

The interpretation is contested in a way the behaviour is not. Later experiments argue that what looks like Bayesian updating fits a simpler rule of thumb, and one line of work elicited beliefs to separate cascades from plain imitation. None of those papers was read here. Baddeley makes the same observation: the laboratory finding has been replicated widely, and few replications rigorously tested alternative hypotheses.

Cai's plaque: herd behaviour that worked

If independence is what matters, the test is a case where the social information was true. Hongbin Cai, with Yuyu Chen and Hanming Fang, ran that case. In Beijing restaurants they placed a randomised plaque on the table listing the five most popular dishes, in a design built to separate observational learning from the mere salience of seeing a dish named. Demand for the listed dishes rose by 13 to 20 per cent. Naming sample dishes without the ranking produced no significant saliency effect.

Two further results make it the best-identified study available to us. The effect was modestly stronger among infrequent customers, which is what the theory predicts, since social information is worth most to the person whose own signal is weakest. And dining satisfaction rose with the top-five plaque, while the sample names moved it nowhere. Herd behaviour made the meal better.

The field work is also older than the social-media story suggests. Ward Hanson and Daniel Putler inflated the download counts of software on a large commercial online service in 1996, manipulating one member of each matched program pair at randomised levels, and induced substantial additional downloads. Substantial is their word, the body text is paywalled, and no magnitude appears here. Their closing line asked for verifiable online popularity measures. Thirty years on, nobody has built them.

Whether people weight social information sensibly at all was tested by Thomas Morgan and colleagues, who carried nine predictions from the formal models into computer-based tasks. Demonstrator numbers, the consensus among them, task difficulty, the subject's own confidence and the cost of working the answer out alone all influenced how much social information people used, and did so adaptively. No sample size or effect size was obtained at source, and the result is about averages rather than about any particular person. Crowds as a sign of worth are tested in an article on [whether a long queue makes people want in](https://thewhyweproject.com/articles/does-a-long-queue-make-people-want-in).

Muchnik's asymmetry, Deutsch's anonymity

True social information and the appearance of it look identical from the table, which is the problem the next study solves. Lev Muchnik, with Sinan Aral and Sean Taylor, worked with a social news aggregator whose administrators arbitrarily up-voted, down-voted or left alone the first comment on more than 100,000 posts. A fabricated first up-vote inflated the scores that followed, while a fabricated down-vote was corrected away, because other readers pushed back against a rating they thought unfair. The two figures everybody quotes, a 32 per cent rise in the likelihood of a positive rating and final ratings 25 per cent higher on average, are in the published abstract.

Deutsch's anonymity condition, and what it separates

The asymmetry is the discriminator. Pure information-weighting predicts symmetry: a signal is a signal, and a negative one should move you as much as a positive one of the same size. It did not. What moved was the willingness to agree with approval and to resist disapproval, which is a social motive, and social motives run on beliefs about [what everyone else wants](https://thewhyweproject.com/articles/everyone-thinks-everyone-else-wants-it).

A signal is a signal, and a negative one should move you as much as a positive one of the same size. It did not.

Morton Deutsch and Harold Gerard built the instrument for separating the two influences in 1955, running modifications of the Asch task face to face, anonymously, and with self-commitment. Anonymity strips the standing out of a judgement and leaves the information in place. The familiar result, that conformity falls when responses are private with a residue surviving anonymity, reaches us only through secondary summaries, because the abstract deposited for that paper is truncated before its results, and no percentage appears here.

Rod Bond and Peter Smith's meta-analysis of 133 line-judgment studies across 17 countries supplies the second thing a pure information account struggles with. Conformity in the United States declined across the decades after the 1950s, and collectivist countries showed higher conformity than individualist ones. A norm drifts with a culture. A calculation does not. Their abstract also records that Asch himself was much concerned with what allowed individuals to resist group pressure, which is some distance from the way the result is usually retold.

Baddeley's cost, Nielsen's wrong measure

Grant all of that, and the question becomes where the damage falls. Michelle Baddeley's answer relocates the harm, and it is the most useful argument in Copycats and Contrarians. Even when the herd is heading the right way, the private information each copier discarded is lost to everybody standing behind him. It is a cost nobody pays and everybody bears, which is why the cascade result concerns efficiency rather than accuracy.

The money version has a named loser. Amil Dasgupta, with Andrea Prat and Michela Verardo, examined US institutional holdings from 1983 to 2004 and found that stocks persistently bought by institutions over the previous three to five quarters underperformed the market over the following 12 to 30 months, with persistently sold stocks doing the reverse, and that institutions traded in the direction of past institutional trades. Their own explanation is career-concerned trading by delegated managers. A manager who loses money while his peers lose money keeps his job. The authors also flag that single-quarter institutional herding predicts short-term returns positively, so the two horizons point opposite ways and the indictment stays untidy.

Which brings the trade figure, the one claim here read in full at source. Ninety-two per cent gets quoted whenever somebody wants to justify social proof. It comes from a Nielsen market-research report rather than a peer-reviewed paper, and it traces perfectly: more than 28,000 respondents across 56 countries, fielded in August and September 2011, weighted to internet consumers, with Nielsen's own sentence that the survey is based on respondents with online access only. The item measured was recommendations from people I know. Consumer opinions posted online sat separately, at 70 per cent.

What it measures is stated trust in a channel. Nobody in that survey did anything, and the recommendations are mostly from people whose independence a reader can check, which is the one case where the cascade mechanism is least likely to be running. The number is sourced better than most trade statistics and answers a different question from the one it is deployed to settle.

Our position sits between the two camps. The popular framing, in which herd behaviour is a failure of nerve and the sensible person works it out alone, fails in exactly the way the theorems say. The economists' framing, in which copying is simply rational, is incomplete, because Muchnik's asymmetry and Bond and Smith's four decades of drift are both things a pure information account does not predict.

[Whether the crowd picks the best thing](https://thewhyweproject.com/articles/why-the-best-song-does-not-win) is a separate question, and so is [whether you can believe the number](https://thewhyweproject.com/articles/why-we-trust-online-ratings-anyway); this one asks whether the person doing the copying was reasoning badly. Copying is the rational move when the people ahead of you looked at the thing itself, judged it for reasons resembling yours, and left a record nobody paid to place, which is why herd behaviour is not a verdict on anybody's nerve but a question about the provenance of evidence that gets quietly inherited and almost never audited.

Common questions

When is herd behaviour the rational move?

When the people ahead of you chose in sequence, their choices are visible, those choices were made independently on evidence somebody gathered, and their situation resembles yours. Three of those conditions are usually checkable. Independence rarely is, and it decides whether herd behaviour is a sound inference or a habit inherited from whoever went first.

Is herd behaviour the same thing as conformity?

Not reliably. Muchnik and colleagues found that a fabricated first up-vote inflated final scores while a fabricated down-vote was corrected away, and pure information-weighting predicts symmetry between them. Deutsch and Gerard built an anonymity condition to separate the two influences, though the abstract deposited for that paper stops before its results. The distinction is measurable rather than rhetorical.

Do 92 per cent of people trust recommendations from friends?

Ninety-two per cent of more than 28,000 respondents across 56 countries told Nielsen in 2011 that they trusted recommendations from people they know above other advertising. It is stated trust in a channel rather than recorded behaviour, the panel had online access only, and consumer opinions posted online sat separately at 70 per cent.

What is an information cascade?

The state in which somebody who has watched enough earlier choices finds it optimal to follow them whatever his own private signal says. His choice then carries no information about that signal, so the person behind him learns nothing, and the crowd rests on the first few signals.

Sources

Banerjee, A. V. (1992). 'A Simple Model of Herd Behavior.' Quarterly Journal of Economics, 107(3), 797-817. doi:10.2307/2118364

Bikhchandani, S., Hirshleifer, D., & Welch, I. (1992). 'A Theory of Fads, Fashion, Custom, and Cultural Change as Informational Cascades.' Journal of Political Economy, 100(5), 992-1026. doi:10.1086/261849

Anderson, L. R., & Holt, C. A. (1997). 'Information Cascades in the Laboratory.' American Economic Review, 87(5), 847-862

Hung, A. A., & Plott, C. R. (2001). 'Information Cascades: Replication and an Extension to Majority Rule and Conformity-Rewarding Institutions.' American Economic Review, 91(5), 1508-1520

Hanson, W. A., & Putler, D. S. (1996). 'Hits and misses: Herd behavior and online product popularity.' Marketing Letters, 7(4), 297-305. doi:10.1007/BF00435537

Cai, H., Chen, Y., & Fang, H. (2009). 'Observational Learning: Evidence from a Randomized Natural Field Experiment.' American Economic Review, 99(3), 864-882. doi:10.1257/aer.99.3.864

Muchnik, L., Aral, S., & Taylor, S. J. (2013). 'Social Influence Bias: A Randomized Experiment.' Science, 341(6146), 647-651. doi:10.1126/science.1240466

Deutsch, M., & Gerard, H. B. (1955). 'A study of normative and informational social influences upon individual judgment.' Journal of Abnormal and Social Psychology, 51(3), 629-636. doi:10.1037/h0046408

Bond, R., & Smith, P. B. (1996). 'Culture and conformity: A meta-analysis of studies using Asch's (1952b, 1956) line judgment task.' Psychological Bulletin, 119(1), 111-137. doi:10.1037/0033-2909.119.1.111

Morgan, T. J. H., Rendell, L. E., Ehn, M., Hoppitt, W., & Laland, K. N. (2012). 'The evolutionary basis of human social learning.' Proceedings of the Royal Society B, 279(1729), 653-662. doi:10.1098/rspb.2011.1172

Dasgupta, A., Prat, A., & Verardo, M. (2011). 'Institutional Trade Persistence and Long-Term Equity Returns.' Journal of Finance, 66(2), 635-653

Nielsen (2012). Global Trust in Advertising and Brand Messages. April 2012

Related concepts

• Information Cascades
• Normative Social Influence
• Reputational Herding
• Rational Herding

People

• Rod Bond
• Abhijit V. Banerjee