sign in sign up
<<
Home , Information cascade

540 Cascades and Rational

Information Cascades and Intermediate article Rational Conformity Lisa R Anderson, College of William and Mary, Williamsburg, Virginia, USA Charles A Holt, University of Virginia, Charlottesville, Virginia, USA

CONTENTS Introduction Applications to markets and other social Conformity incentives Conclusion Rational information cascades

An is a pattern of matching attempts to explain temporary patterns in invest- decisions. A cascade can occur when people ob- ment behavior. serve and follow `the crowd', which can be rational if the information revealed in others' earlier decisions outweighs one's own private information. CONFORMITY INCENTIVES There may, of course, be non-informational factors INTRODUCTION that produce conformity in social interactions. Sometimes people prefer to behave like the others When individuals obtain private information and in a group. Such behavior has even been recom- make publicly observed decisions in a sequence, mended (Post, 1927, chap. XXXIII): `to do exactly as the first decisions tend to act as `signals'. If early your neighbors do is the only sensible rule'. decisions show a clear pattern, the information There may be social stigmas and inferred from them may outweigh any one person's associated with nonconformity. For example, an private information. This inference can cause people economic forecaster may prefer the chance of to `follow the crowd', even when the group consen- wrong with everybody else to the risk of sus conflicts with their own private information. providing a deviant forecast that turns out to be This type of sequential conformity is termed the only incorrect guess. In the words of John an `informational cascade' in a seminal paper by Maynard Keynes (1936, p. 158): `worldly wisdom Bikhchandani et al. (1992). teaches that it is better for reputation to fail conven- For example, consider an employer who inter- tionally than to succeed unconventionally'. views a job applicant and forms a good impression. Some research suggests that people prefer to The employer, however, does not offer the job after maintain the status quo (Samuelson and Zeckhau- discovering that the worker has been turned down ser, 1988). For example, subjects in experiments previously by other employers. Even though this were provided with a scenario in which they in- decision is in conflict with the employer's own herit a portfolio of cash and securities and are information, it may be rational if the employer asked whether to leave the portfolio intact or to concludes that the other interviews went badly, change it by investing in other securities. There and that the aggregate information implied by was a strong tendency for individuals to retain past interviews more than offsets the employer's portfolio A in preference to B when it was listed own positive evaluation. Even a qualified applicant as the current portfolio, and to retain portfolio B in may make a bad impression on any given day, so preference to A when it was listed as the current may have difficulty finding a job after several portfolio. A similar tendency was observed in unsuccessful attempts. response to other matched pairs of questions that Bannerjee (1992) uses the term ` behavior' alternated descriptions of the status quo choice. to describe similar patterns of conformity that arise Such a `status quo ' may explain herding in models where individuals must decide which behavior in sequential decision situations. But type of financial asset to purchase. Indeed, much these decision patterns do not allow us to distin- of the interest in cascade behavior arises from guish between behavior based on a preference for Information Cascades and Rational Conformity 541 conformity and behavior that is motivated by This example was used by Anderson and Holt information inferred from prior decisions. Thus, (1997) in a laboratory experiment in which subjects someone inheriting a portfolio from a rich uncle were paid a cash reward for each correct predic- might conclude that the uncle's wealth was due tion. The events were referred to as `urn A' and to wise portfolio choices that should be imitated. `urn B'. Each urn was a cup with three colored Laboratory experiments can be used to up balls, which we will refer to as a or b signals. and control information flows in order to dis- There were two a balls and one b ball in urn A, tinguish among alternative of herding and there were two b balls and one a ball in urn B. behavior. A random device was used to select the urn, with each event being equally likely, and therefore, each RATIONAL INFORMATION CASCADES of the six balls is equally likely to be drawn. Sup- pose that the draw is b. Since two of the three b balls We will use a numerical example to illustrate the are in urn B, the posterior probability of urn B given 2 of a rational information cascade (Ander- a draw of b is 3. (This is an example of the applica- son and Holt, 1997). In this example, there are two tion of Bayes' rule; or more precisely, the ball- equally likely events, A and B, which might repre- counting heuristic used here corresponds to the sent whether or not a particular patent is market- conditional-probability calculations that are re- able. Decision-makers obtain private signals, a and ferred to as Bayes' rule. See Holt and Anderson b, which are correlated with the events. In particu- (1996) for a discussion of how the simple counting 2 1 lar, P(ajA) ˆ P(bjB) ˆ 3, so the error rate is 3 for heuristic can be used to make Bayesian calculations each signal. (For example, the signal might be the in more complicated settings, and an intuitive ex- result of a consultation with experts.) This model planation of the mathematical expression of Bayes' assumes that each person's private signal is correl- rule.) Of course, it is intuitively obvious that the 1 ated with the event but is independent of the other probability of urn B is greater than 2 when the signals. After observing their signals, individuals signal is b. Holt and Anderson (1996) show that 1 are approached one by one in a sequence and are the probability of urn B is still greater than 2 when asked to make a prediction about which event has first two predictions are B and the third person's occurred. People find out the prior predictions, signal is a. Thus, a cascade can begin with two if any, made by others, but they cannot observe matching decisions, and all subsequent decision- others' private signals. Thus the prediction made makers should follow the pattern established in by the first person is based only on that person's this manner. signal, and hence will reveal that signal, since the Information cascades may not form immediately signal is more likely to be correct than not. if there is not a bias in early predictions. Suppose, Suppose the first person sees a b signal and pub- for example, that the first two predictions are A and licly predicts event B. If the second person in the B, so the third person would consider each urn to sequence sees a b signal, it is rational for this person be equally likely, prior to seeing a private signal. If to also predict B. If the second person sees an a the third and fourth decision-makers both predict signal, the observed and inferred signals essentially B, then this bias in favor of B would cause the fifth cancel each other, and each state is equally likely. person to predict B, regardless of that person's We observe from laboratory experiments that indi- private signal. viduals almost always use their own information in These calculations are based on a model of per- such cases, and therefore, the second decision will fect rationality. The purpose of an experiment is to reveal the person's private signal, whether or not it determine how people actually behave in such situ- conforms to the first prediction. When the first two ations. Anderson and Holt (1997) used the `ball and individuals in the sequence observe the same urn' scenario described above in order to remove signal, their decisions will also match. In this case, any preference for conformity that is not based on the information inferred from the matching deci- informational considerations. Subjects were placed sions is greater than the information inferred from in small cubicles and were shown a single ball any one private signal. In particular, if the first two drawn from the relevant urn, but they could not people choose B, then the third person should also see which urn was being used. Subjects were choose B, even if that person's private signal is a. selected in a random order to make their predic- Information cascades form in this manner, and the tions, which were announced by a neutral assistant effect is that all subsequent decision-makers will who did not know the signals or which urn was follow a pattern established by the first ones in being used. (Allowing subjects to announce their the sequence. own predictions could have given them the chance 542 Information Cascades and Rational Conformity to convey additional uncontrolled information, by optimal Bayesian prediction is to follow the estab- tone of voice, for example.) After all predictions lished pattern, but subjects deviated in about a had been announced, a non-decision-making sub- quarter of the cases in which their own private ject serving as a `monitor' announced which urn information was inconsistent with this pattern. had actually been used. Those with correct predic- In summary, the general tendency was for sub- tions were paid $2, and others earned for jects to use the information implied by previous that trial. There were 15 trials and six decision- decisions correctly, which produced rational infor- making subjects in each session. Altogether, there mation cascades. There were, however, deviations were 12 sessions in the experiment, each of which that could either break a cascade or result in an was conducted on a different day. incorrect cascade. Incorrect cascades also occasion- The sequences of draws made cascades possible ally resulted from `unlucky' incorrect decisions in more than half of the trials, and cascades actually observed by early decision-makers. formed in about 70% of the trials in which they This pattern of results was replicated by Hung were possible. A particularly interesting trial is and Plott (2001), who added some interesting treat- shown in Table 1. In this case, all six individuals ment variations. In one of their experiments, the earned $2, since urn B was actually used for the incentive structure was altered so that subjects draws. received a positive pay-off only if the majority of Generally, prior information is informative, and the group made the correct prediction. (This is cascade behavior tends to increase the accuracy somewhat like a jury whose decision is determined of predictions, and hence to increase earnings. It by a majority vote.) The effect was to reduce con- is possible, however, for initial predictions to be formity for early decisions because individuals incorrect, which may create an incorrect cascade. have an incentive to signal their information so This occurred in another trial, shown in Table 2. In that others can make better decisions. A second this case the first person's prediction revealed their treatment rewarded conformity directly: subjects signal, but the second person made a serious error received a positive pay-off only if their decision in predicting B after seeing an a signal and a prior A matched that of the majority. prediction. The third person predicted B, which was also an error, since previous predictions were APPLICATIONS TO MARKETS AND balanced and their own signal suggested urn A. All OTHER SOCIAL INSTITUTIONS of the remaining individuals predicted B, which turned out to be incorrect, since urn A was used. Strong movements in stock prices are sometimes The most common type of error occurred when a attributed to herd-like behavior. Keynes (1936) person saw a signal that was inconsistent with the noted the similarity between investment decisions implication of prior predictions. In this case, the and a guessing in which participants have to predict which contestant in a contest will get the most votes. In this game, each person has to Table 1. A trial from Anderson and Holt's (1997) `ball think about whom the others think is attractive, and urn' experiment. Three of the last four decision- and also about whom the others think others will makers follow the pattern established by the first two find attractive, and so on. Similarly, when investing despite contradictory in stocks, one would like to guess which enterprises will become popular with other investors, since a Subject 58 57 59 55 56 60 strong demand will raise the prices of those stocks. Observes bbabaaA herd-like response may move asset prices out of Predicts B B B B B B line with market fundamentals, and thus set the stage for an equally strong `stampede' in the other direction. Such behavior could be due to seemingly irrational `animal spirits', to use Keynes's colorful Table 2. A trial from Anderson and Holt's (1997) `ball term, or it could be due to a rational tendency to and urn' experiment. The second and third subjects both follow others' decisions when they are based on made errors, which led to an incorrect cascade (urn A independent sources of information. Christie and was used) Huang (1995), for example, argue that it can be Subject 57 58 59 55 60 56 rational to follow others' decisions during surges Observes aaaaaaor declines in stock prices; i.e., to rely on inferences Predicts A B B B B B derived from information that is aggregated by market prices. Information Cascades and Rational Conformity 543

Other applications are suggested by the majority- given only the person's own private signal. This voting treatment of Hung and Plott (2001). In a type of `information cascade' can produce con- trial, for example, jurors may form independent formity that is rational, because the information judgments about the or innocence of a defend- content in prior decisions may outweigh that in ant, but such judgments are often changed in the one's own private signal. There is some laboratory process of voting and deliberation. In this manner, evidence to support such theories of rational cas- can create the consensus needed to cades, although individuals do make mistakes, avoid a `hung jury'. Some experiments that simu- and behavior is sometimes influenced by late sequential jury voting have been conducted, and heuristics that may lead to non-Bayesian and strong patterns of cascade-like conformity are decisions. observed in many cases. Decisions may occur in sequence in these appli- References cations (e.g., as stock purchases appear on a ticker tape), but the order of decisions is not exogenously Anderson LR and Holt CA (1997) Information cascades in the laboratory. American Economic Review 87: 847±862. specified as it was in the experiments discussed Bannerjee AV (1992) A simple model of herd behavior. above. The order of voting is not exogenous in Quarterly Journal of 107: 797±817. jury voting unless the foreman chooses to take Bikhchandani S, Hirshleifer D and Welch I (1992) A votes by going around the table. Similarly, stock theory of fads, fashion, custom, and cultural change as purchases or responses to initial public offerings informational cascades. Journal of Political Economy 100: are not subject to order requirements. Plott et al. 992±1026. (1997) report some pari-mutuel betting experi- Christie WG and Huang RD (1995) Following the Pied ments with an endogenously determined order of Piper: do individual returns herd around the market? . The incentive structure is like that of a horse Financial Analysts Journal 51: 31±37. race in which the purse is divided among those Holt CA and Anderson LR (1996) Classroom : who bet on the winning horse, in proportion to understanding bayes' rule. Journal of Economic Perspectives 10: 179±187. their bets. The experiment was presented as a Hung AA and Plott CR (2001) Information cascades: choice between six assets, with only one of them replication and an extension to majority rule and offering positive earnings, depending on the real- conformity-rewarding institutions. American Economic ized state of . Investors had private, noisy Review 91: 1508±1520. information about the assets, and they could ob- Keynes JM (1936) The General Theory of , serve others' bets as they were made. A consider- Interest, and Money. London, UK: Macmillan. able amount of information aggregation was Plott CR, Wit J and Yang WC (1997) Paramutuel betting observed in these experiments, with the asset prices markets as information aggregation devices: accurately indicating the correct state in most cases. experimental results. Working Paper, California In some cases, however, heavy purchases of an Institute of Technology. asset triggered more purchases, even though the Post E (1927) in Society, in Business, in Politics, and at Home. New York, NY: Funk and Wagnalls. asset being purchased turned out not to be the Samuelson W and Zeckhauser R (1988) one that paid off. This corresponds to an incorrect in decision making. Journal of Risk and Uncertainty cascade. The application of information cascade 1: 7±59. theory to asset markets in richer and more realistic settings is a prime area for research. Further Reading CONCLUSION Anderson LR (2001) Payoff effects in information cascade experiments. Economic Inquiry 39: 609±615. Theoretical models of `herding' pertain to situ- Anderson LR and Holt CA (1996) Classroom games: ations where individuals observe private signals information cascades. Journal of Economic Perspectives 10: that are correlated with some unknown event. Pre- 187±193. dictions about the event are made in sequence, with Asch SE (1952) . New York, NY: later decision-makers being able to base their pre- Prentice-Hall. Asch SE (1956) Studies of independence and conformity: dictions on their own signal and on information a minority of one against a unanimous majority. inferred from prior decisions. The first few deci- Psychological Monographs 70(9). sions tend to reveal the private signals, which may Camerer C (1995) Individual decision making. In: Kagel establish a pattern of matching predictions that JH and Roth AE (eds) The Handbook of Experimental others follow, even if the conforming predictions Economics, pp. 587±703. Princeton, NJ: Princeton are different from the prediction that would be best University Press. 544 Information Cascades and Rational Conformity

Davis DD and Holt CA (1993) Experimental Economics. Pound J and Shiller RJ (1989) Survey evidence on Princeton, NJ: Princeton University Press. diffusion of interest and information among investors. Devenow A and Welch I (1996) Rational herding in Journal of Economic Behavior and Organization 12: 47±66. . European Economic Review 40: Thaler RH (ed.) (1993) Advances in Behavioural Finance. 603±615. New York, NY: Russell Sage Foundation. Kahneman D and Tversky A (1973) On the psychology of Welch I (1992) Sequential sales, learning, and cascades. prediction. Psychological Review 80: 237±251. Journal of Finance 47: 695±732.

Information Processing Intermediate article James T Townsend, Indiana University, Bloomington, Indiana, USA Kan Torii, Indiana University, Bloomington, Indiana, USA

CONTENTS Definition and Codes in information processing Serial and parallel processing, flow diagrams, and Systems-factorial for determining continuous-flow systems architecture Independence, capacity, and stopping rules Conclusion Mathematical models of human information processing and cognition

The information-processing approach in cognitive early and continued use led to the term `process science assumes mental architectures with various model', again suggesting a model or theory that components that interact in order to manipulate tells what happens cognitively across . A incoming information. `model' is a theory constructed to explain and make predictions about a relatively restricted set DEFINITION AND HISTORY of phenomena, while a `theory' may aim to cover a much wider range. However, the terms `model' Any field of study, in this case cognitive science, and `theory' are often used interchangeably. Much always has as a backdrop a kind of super-theory or of psychology has traditionally been oriented more metatheory, which may itself be rather vague but towards static descriptions (e.g., most personality which provides a or way of thinking trait models are static in nature), so the of about problems and helps to motivate the theoret- being composed of active processes was a major ical and experimental investigations that are carried innovation in the study of human thought and out. The information-processing approach is a good behavior. The words `coordinated operation' also candidate for the central metatheory of cognitive suggest that the model builder is paying close at- science. Cognitive science began to emerge, slowly tention to how the operations of the various com- at first, in the 1950s, and developed rapidly in the ponents involved in a mental task might start, 1960s and 1970s, becoming the dominant continue, and stop relative to each other. A notable in psychology and attracting researchers in linguis- omission in the above definition of information tics, computer science and philosophy. processing is the arrangement, or architecture, of A popular introductory text on cognitive science the processes. Architecture has been the subject of (Ashcraft, 2002) defines the information-processing many studies. approach as `the coordinated operation of active In the 1950s, a number of well-known experimen- mental processes within a multicomponent mem- tal (and early cognitive) psychologists employed ory system'. The essential element of this definition information theory (e.g., Shannon and Weaver, is the specification of `active mental processes' in- 1949) as a theoretical and methodological tool. dicating dynamic ongoing activity. The term `pro- Claude Shannon, an engineer, invented informa- cesses' emphasizes this dynamic aspect, and its tion theory to measure how much information is