Now we know more about how Bayesian reasoning works, let us return to the problem of reconciling conflicting evidence about the relative merits of Benito’s and Amigo’s. We start with a prior probability: most people preferred Amigo’s in the past. Private information from a restaurant review we have read contradicts this. Then new information comes along in the form of social information about other people’s restaurant choices. Using Bayesian reasoning, we update our estimate of the chances that one restaurant is better than the other to form a posterior probability. We reassess our initial judgement, deciding that the balance of private information and social information indicates that Amigo’s is the restaurant to choose. We might reach the opposite conclusion if we could see everyone’s private information – but we can’t.
Herding games
If herding and information cascades are driven by people cleverly using Bayes’ rule, then herding is not necessarily an irrational phenomenon. Nevertheless, whilst we have learnt that rational herding is a theoretical possibility, we have not established empirically that herding is rational. What is the evidence, either way? Across the social sciences, the answers are mixed. Some economists have collected evidence to suggest that herding is rational. But many other social scientists have collected evidence to suggest that it is not – as we shall see in the next chapter. Here, let’s focus on the economists’ evidence, and in subsequent chapters we will attempt to reconcile this with the conflicting evidence from other social scientists.
One piece of evidence comes from studying real-world restaurant queues. Behavioural economists Arthur Fishman and Uri Gneezy had a clever idea for a natural experiment to test for social learning about restaurant choices.12 They recruited some research assistants to watch people choosing between two very similar fast food restaurants in an outdoor food court next to Bar Ilan University in Tel Aviv. They incorporated two observation periods into their study in order to capture how the impact of social influences shifted as people had more opportunity to learn for themselves which restaurants were better. As these restaurants were next door to a university, Fishman and Gneezy assumed that, at the beginning of the academic year, a larger proportion of customers would be new students (and so far less well informed about the restaurants’ quality). So they observed one group of 1,324 customers in October 2009 (the beginning of Bar Ilan’s academic year) and a second group of 1,153 customers around mid-April 2010 (the end of Bar Ilan’s academic year).
Fishman and Gneezy discovered that there were big differences in the length of the queues of customers waiting for a table in the two restaurants. In October, the queues outside the crowded restaurant were much longer than those outside the emptier restaurant. By April, however, the queues were much more equal in length: whether the restaurant was crowded or empty was not making much difference to the queues’ length. Fishman and Gneezy explained that social learning could explain the disparity. If the student customers had no prior knowledge and were inferring nothing from the choices of other customers, then they should have chosen randomly in October. The fact that they distributed themselves unevenly, joining long queues for the restaurant that was already popular and crowded, suggested that something else was driving them. Given that the only information available was the social information implicit in the choices of other customers, Fishman and Gneezy concluded that the queue was the trigger. Perhaps new students were using the social information conveyed by long queues as a signal of quality: a real-world example of an information cascade. By April, however, perhaps the students had had a chance to learn more for themselves about the two restaurants and so were less reliant on learning by observing others’ choices, so the lengths of the two restaurant queues became much more similar.13
The American economists Charles Holt and Lisa Anderson, from the University of Virginia and the College of William & Mary respectively, explored the social learning, information-cascade hypothesis using controlled laboratory experiments. Holt is an experimental economist well known amongst economics lecturers for developing a wide range of engaging experiments, many of which are suitable for students to use in a classroom setting.14 His experiments with Anderson were designed as a rigorous test of whether or not information cascades are consistent with Bayes’ rule. Anderson and Holt’s basic design has been widely replicated and refined in subsequent experimental studies, making it a very influential study for economists interested in herding.15
Anderson and Holt brought together seventy-two students to play a guessing game, with cash rewards for correct guesses. The students were shown two urns, Urn A and Urn B. Urn A contained two red balls and one black ball. Urn B contained two black balls and one red ball. Without the students seeing, the experimenters poured the contents of one of the urns into an unmarked urn. The students were then challenged to guess if this unmarked urn contained the contents of Urn A or Urn B.
To simulate an information cascade, the students did not guess all at once. They were asked to form a queue and guess one by one. They were given some extra pieces of information – some private, some social – to help them decide. The students got their private information from being invited to go up to the unmarked urn individually, pick out a ball, check its colour and then put it back, without letting any of the other students know the colour of the ball they had chosen. Each student then announced their guess of Urn A or Urn B to the group. One by one, the students were inferring something from the social information they were accumulating as they learnt about the other students’ guesses. Anderson and Holt postulated that the students were engaged in a process of Bayesian updating. Each student would form a prior probability based on what they knew at the outset. They updated this prior probability each time they heard another student’s guess, and when they picked a ball themselves.
Figure 2. The urn game: players are asked to guess which urn’s contents are in the unmarked urn: Urn A (2 red balls, 1 black ball) or Urn B (2 black balls, 1 red ball)?
How does a Bayesian information cascade unfold in the urn experiment? Let us put ourselves in the shoes of the second student to decide, Bob. The first student, Alice, has already announced her guess – Urn A. Bob infers that this must be because she has selected a red ball, as there are more red balls than black balls in Urn A. Bob then draws a red ball from the unmarked urn. He now has two pieces of information: first, social information from Alice’s guess of Urn A; second, private information from his own private selection of a red ball. Luckily for Bob, the guess is relatively easy because the social information and private information are consistent. He guesses Urn A. His guess is not definitely correct, but it is more likely to be correct than a guess of Urn B – which he would have no justification for making, because so far he has no evidence at all that the urn is more likely to be Urn B.
We can change the scenario to make it harder for Bob and to illustrate Bayesian principles. Let’s assume it is Urn B, but that Alice’s guess does not change: she guesses Urn A, so Bob infers that she did pick a red ball – by no means an impossible scenario given that one of the three balls in Urn B is red. But Bob picks a black ball. Now he is confused. What should he do, given these mixed signals? Should he go with Alice’s guess of Urn A? Or should he guess Urn B, given that the black ball he has chosen is more likely to come from Urn B? If he guesses Urn A, he is discounting his private information – the evidence from his own eyes of a black ball. But if he guesses Urn B, then he is disregarding the information implicit in Alice’s guess. For Bob, applying Bayes’ rule could rationally justify either answer.
Let’s assume that he decides to favour the social information from Alice and guesses Urn A. Then a Bayesian information cascade will start to build. The third student, Chris, draws his ball and perhaps again picks a black ball. Chris has three pieces of information. Alice has picked Urn A, and so has Bob: Chris assumes that this is because they have picked red balls. Chris, however, has picked a black ball – one piece of information that suggests Urn B, against the two inferences he make
s from Alice and Bob’s guesses of Urn A. The balance of evidence has shifted in favour of Urn A, even though that is not the right answer. If Chris is using Bayes’ rule then the only conclusion he can reach is that he should guess Urn A. For Chris and all the students still waiting to guess, rationally that is the best guess they can make. The information cascade reinforces Alice’s mistaken guess of Urn A. So, no student will win a cent if they are using Bayes’ rule to decide. This information cascade has led the herd in completely the wrong direction and the pinch point was Bob’s choice, when the guesses were on a knife-edge. If Bob had instead favoured his private information and correctly guessed Urn B, then all the students except Alice would have won money for correct guesses (and it would have turned into a very expensive experiment for the researchers).
Anderson and Holt analysed all the evidence from their experiment to assess whether the students were deciding in a way that was consistent with the Bayesian information cascade models described above. They found that information cascades unfolded in a way that was consistent with Bayes’ rule in forty-one out of the fifty-six times when the private information and social information were inconsistent – that is, in the sort of situation Bob faced when he saw a black ball alongside inferring that Alice had seen a red ball.
What of the fifteen of the fifty-six times when the information cascades were not consistent with Bayes’ rule? What explains those guesses? Were some students better at using Bayes’ rule than others? Do the anomalous findings suggest that some people place different weights on private and social information? Could students have been using a simpler rule of thumb to decide, and this rule, just by coincidence, generated guesses that mimicked Bayesian guesses?16 Anderson and Holt’s experimental findings have been replicated across a wide range of other studies but not many have rigorously tested alternative hypotheses. Do most of us use Bayes’ rule to process social information? Or do we use other tools to guide our choices? Economic theory does not answer these questions, and so we shall go beyond economics to explore some answers from other disciplines in the following chapters.
Is social learning good or bad?
From an economist’s perspective, is following the herd rational or irrational?17 If the herd goes in the wrong direction, then that is obviously bad: a large group of people have made the wrong choice. But even if the herd is on the right track, there will nonetheless be negative impacts because valuable private information is lost when people disregard it in the process of following a herd. We can use our restaurant example to illustrate the point. Once the information cascade favouring Amigo’s takes hold it will continue until everyone has chosen Amigo’s. At the end of this process, many pieces of useful, rich, privately held information will have been discarded by the herd. A negative, suboptimal outcome has emerged because individuals have favoured social information over important, useful but unobservable private information.18 As individuals’ private information is lost during herding, there are negative external consequences for the group – what economists call negative externalities. Restaurant-goers have forgone an opportunity to try Benito’s and discover how good it is. If they had chosen it, Benito’s would have justly benefited from increased takings and the buzz of popularity. Those enjoying Benito’s might later have had a chance to share their good experiences with friends and family, and with others more widely via online reviews. There would have been many winners and only one loser (Amigo’s) if the herd had headed in a different direction.
Perhaps counterintuitively, these negative consequences do not disappear just because the herd has identified the better path. A subtler point is that, even if the herd had headed in the right direction in choosing Benito’s, private information would still have been lost and overwhelmed by social information. Imagine that one of the people who had some private information suggesting Benito’s was better had been the first to choose which restaurant to eat in, thereby setting off the unfolding of an information cascade that ensured the herd made the right choice. The point is not so much about whether the herd does the right or wrong thing in the end, or whether each person has decided in a logically rational way. The problem is that rich stores of private information are lost via this mechanical Bayesian updating process.
We can illustrate the importance of private information if we change our restaurant scenario a little. Imagine that the first person to choose hasn’t read a biased online review but instead has read a very recent review written just after Amigo’s had sacked its cook and enticed Benito’s brilliant chef away with a promise of better pay and working conditions. So, the good review for Benito’s, read by us and most of the others waiting, was based on inaccurate, out-of-date information. The first person to choose had better private information, i.e. a bang-up-to-date and possibly more accurate review. Still, perhaps the brilliant chef will not do so well at Amigo’s if Amigo’s has other problems besides the cook they have just sacked – poor management practices, perhaps. Either way, a rich, diverse set of private information is helpful or, at the very least, might help each restaurant-goer to know that there isn’t unanimous agreement about which restaurant is better. Any and all of this information is lost once the information cascade takes hold.19
So, self-interested herding driven by social learning can create distortions. Are other forms of self-interested herding less problematic? Some can be helpful for the group as well as the individual. To see how this works let us turn to some of the other economic incentives and motivations behind self-interested herding. There are strategic advantages when we copy others, linking to the benefits we gain by using herding as a form of signalling. Self-interested herding can be a means to build our reputations. Powerless individuals can gather together in a powerful herd. Herds are sometimes havens for safety.
Strategic advantages
The strategic advantages that we can accrue if we join a group or herd have been extensively explored by game theorists.20 The basic idea is that a selfish individual can hook up with other selfish individuals and together, as a group, they can do much more than each person could do alone – for example, when hunting. In his 1755 masterpiece, A Discourse on Inequality, philosopher Jean-Jacques Rousseau used a ‘stag hunt game’ to illustrate how coalitions form for the benefit of each member.21 Four hunters are deciding whether to hunt as individuals or to collaborate and hunt as a team. No one hunter can catch the stag alone because it is so big and fast. If they hunt as individuals the best they can hope for is to catch a hare. One hare is not even enough to feed a single family. A much better outcome would be for all four hunters to join forces and catch a stag together. A stag would be more than enough to feed four families, whereas a single hare would leave each family hungry. So the hunters form a coalition. Assuming the four hunters can negotiate an equitable division of their hunting spoils, then their coalition will prosper. The benefits of working together for the individual members of the coalition are greater than if each of them had hunted alone. It is in the individual’s self-interest to join the hunt: everyone’s a winner (except the stag).
Groups of self-interested individuals do not always deliver a good collaborative outcome, however. When people work together they interact, and so selfish individuals can affect the actions and performance of the group as a whole. When outputs and rewards are shared in a team, the individual team member may have incentives to shirk and free-ride on the efforts of others. Self-interested individuals will subvert the efforts of the team, unless everyone’s incentives are somehow aligned. This insight about strategic advantage parallels economists’ models of rational herding as a response to the extra benefits that can come from copying other people’s choices. The most common example is the additional payoffs that accrue in financial markets when a series of financial traders are buying into a rising market, each helping an asset’s price to rise and thus benefiting the whole herd of traders. We shall explore these related financial herding phenomena in chapter 6.
Signalling
Ano
ther manifestation of self-interested herding is the copying behaviours we use as signals to others around us.22 For example, unconventional behaviour can be used as a signal of authenticity and commitment to groups defined by their rebellion against society’s norms. Twentieth-century youth subcultures – from mods and rockers to punks and goths – show how signalling reinforces our sense of identity. In a world of imperfect information and limited trust, we are vulnerable to exploitation by those who can pretend to be what they are not. Behaviours that might seem contrarian to the world at large are crucial signals we send to important subgroups with which we identify; those groups are more likely to trust us if we resemble them, and we are more likely to trust them – to our mutual benefit.
We will explore the perspective of the group in more detail in the next chapter, but some economists have explained how and why we form an identity using the standard economics focus on balancing benefits against costs. In this way, economists George Akerlof and Rachel Kranton explain how we use signals to build identity. Actions that might seem anomalous to outsiders have payoffs for members of a group because they help a person to build their sense of identity with the groups they join. Identity and belonging increase people’s satisfaction and so they will be prepared to incur physical and economic costs in acquiring physical markers that accentuate their sense of belonging to a particular group.23 When and how is it economically rational to signal our identification with others through ostensibly costly and painful actions, such as tattoos and piercings? These seem like maverick actions to outsiders, but make much more sense to others with whom we identify. And the costlier the actions, the better, because more costly signals are more credible. We would not incur such large costs – whether physical, psychological or monetary – if we were not sincere.
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