Rational Herding

What it is

The popular account of following the crowd treats it as weakness. Economics treats it as arithmetic, and the arithmetic wins more often than the popular account allows.

Banerjee's 1992 abstract is short enough to carry the whole argument, and it is worth reading as three separate claims rather than one. A sequential decision model in which each decision-maker looks at the decisions made by previous decision-makers. This is rational for her, because those other decision-makers may hold information that matters to her. Optimising individuals therefore do what others are doing rather than using their own information. And the resulting equilibrium is inefficient.

Read in that order, the gap between the second and third sentences is the whole subject. Nobody in that model is irrational, confused, socially anxious or weak-willed, and the outcome is still worse than the information inside the crowd should allow. The mechanism underneath it is set out on the page for information cascades; this page is about the verdict.

Where the harm actually falls

The most useful thing in the trade literature on this subject is Baddeley's relocation of the damage. The standard social-proof account puts the cost in the individual, who does something suboptimal. She puts it in the aggregate.

Even when the herd is heading the right way, she argues, there are negative consequences, because valuable private information is lost when people disregard it in the process of following. She presses the counterintuitive half rather than softening it: those consequences do not disappear just because the herd has identified the better path. Economists call this a negative externality, and it gives this site a mechanism for why social proof is costly that does not require anybody to be reasoning badly. It also explains why the 1992 result is a statement about efficiency: the crowd may well be right, and it is still carrying less information than it was handed.

The discriminator

If copying can be either a sound inference or a social reflex, and both look identical from outside, the useful question is whether anything separates them in practice. The cleanest available answer is an asymmetry.

Lev Muchnik, 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 in 2013. False positive entries led to inflated subsequent scores. False negative initial votes had small long-term effects, because other readers pushed back against a rating they judged unfair.

A purely informational account predicts symmetry. A signal is a signal, and a negative one of a given size should move you as much as a positive one. It did not. Something asymmetric is operating, and the asymmetry runs in the direction of agreeing with approval and resisting disapproval, which is a social motive rather than an informational one. The two often-quoted percentage figures attached to that paper are not printed here, because they reach this site through the published abstract as quoted in secondary sources and through a co-author's own write-up, and the paper body was not read.

The case where copying plainly worked

Set that beside Hongbin Cai, Yuyu Chen and Hanming Fang's 2009 field experiment, and the argument is complete in two studies. In Beijing restaurants, a randomised plaque listing the five most popular dishes raised demand for them by 13 to 20 per cent. There was no significant effect from merely naming sample dishes, which rules out the explanation that the plaque drew the eye. The effect was modestly stronger among infrequent customers, which is the theory's own prediction, since social information is worth most to the person whose private signal is weakest. And dining satisfaction rose with the top-five information and not with sample dish names, which is the rarest result in this literature: the copying made the outcome better rather than merely more uniform.

Same behaviour, opposite verdict. What differs between the restaurant and the aggregator is whether the social information was independently produced.

And the measurement of whether people do this sensibly

Thomas J. H. Morgan, Luke Rendell, Micael Ehn, William Hoppitt and Kevin Laland tested nine hypotheses drawn from the formal models across several computer-based tasks, reported in Proceedings of the Royal Society B in 2012. The number of demonstrators, the consensus among demonstrators, subjects' own confidence, task difficulty, the number of sessions, the cost of working it out alone, subject performance and demonstrator performance all influenced how much social information people used, and did so adaptively.

That is the pro-rational case at its strongest, because it is the model's predictions put to people and surviving. The limit belongs in the same breath: these were computer-based tasks, and no sample size, effect size or per-hypothesis result was obtained at source, so the finding available here is directional. People weight social information sensibly on average. That is not the same as any particular person doing so on any particular occasion.

In effect

Fund managers who were right about their careers

Amil Dasgupta, Andrea Prat and Michela Verardo examined quarterly United States 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, while persistently sold stocks did the reverse. Institutions traded in the direction of past institutional trades. Their own explanation is a model of career-concerned trading by delegated portfolio managers.

Baddeley puts the incentive in one sentence: a trader who loses a million pounds while his peers are also losing a million pounds will probably keep his job, and a trader who loses a million pounds while others lose nothing will almost certainly be fired. Copying was correct for the manager's career and wrong for the client's money, which is the externality argument with a named beneficiary and a named loser. This variant has its own page at Reputational Herding. Two limits travel with it: the abstract was read at the London School of Economics record for the 2007 working-paper version and the published text was not read, and the authors themselves flag that single-quarter institutional herding predicts short-term returns positively, so the short and long horizons point opposite ways.

Ordering what the next table ordered

The everyday version is the one the theory was built on, and the test it suggests is practical. Before treating what other people chose as evidence, ask whether they looked at the thing or at each other. Baddeley's own refinement sharpens this into a rule: copying is rational in proportion to the complexity of the choice. A fridge is simple enough to judge for yourself, so copying a neighbour's fridge is a worse bet than copying their phone, where the options are genuinely bewildering.

The uncomfortable corollary is that the condition which decides the question is the one you cannot see. You can count the people ahead of you. You cannot audit how they decided.

A trade statistic that traces perfectly and measures something else

Nielsen's Global Trust in Advertising report of April 2012 found that 92 per cent of respondents said they trusted recommendations from people they know, completely or somewhat, against 70 per cent for consumer opinions posted online. That figure is quoted continually as a licence for social proof from strangers.

The report was read in full at source here, and the interesting thing about it is that the provenance is immaculate. Named publisher, dated document, question wording, sample description and a methodology box. The survey was fielded in August and September 2011 among more than 28,000 respondents across 56 countries, with quotas on age and sex based on each country's internet users and weighting to internet consumers, and Nielsen's own sentence states that the survey is based on the behaviour of respondents with online access only. Country inclusion required substantial internet penetration.

So the finding is not that the number is unsourced. It is that the number is sourced perfectly well and is about something else. It measures stated trust in a channel rather than any behaviour, and the headline figure is about friends and family, which is precisely the case where the independence condition is most likely to hold and a cascade least likely to form. The 70 per cent line is the one about strangers. This is a fact about a figure and about how it gets used, and no researcher is at fault for a statistic that was correctly reported and then asked to answer a different question.

What it does not say

It does not say that copying is usually right. It says that copying can be the correct inference, and that the conditions under which it is are checkable in principle and often unavailable in practice.

It does not say that social motives are absent. Muchnik, Aral and Taylor's asymmetry and Rod Bond and Peter Smith's four decades of cultural drift in conformity are both things a pure information story fails to predict, and the economists' framing is incomplete for that reason. Normative influence has its own page at Normative Social Influence.

And the evidence here is graded mixed rather than higher, for a reason Baddeley states about her own subject: rational herding is a theoretical possibility whose empirical base is thin. The theorem is secure. Whether a given real crowd is a rational cascade, a reputational one or simply a crowd is usually not established. No full text was obtained for any of the twelve journal articles behind the article that uses this concept, which is stated here rather than left for a reader to assume otherwise.

Who developed it

Abhijit V. Banerjee published the 1992 sequential model that states the result, and Michelle Baddeley supplies the negative-externality argument that locates the cost in the group. The empirical material on this page comes from Lev Muchnik, Hongbin Cai, Ward A. Hanson, Thomas J. H. Morgan and Amil Dasgupta.

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