1002 JOURNAL OF POLITICAL ECONOMY example with binary signals and a uniform prior on the true value, Welch (1992)has shown that cascades will start and can often be wrong.Banerjee (in press)reaches the same conclusion assuming a continuous uniform prior distribution on the correct action;however, incorrect cascades in his setting derive from a degenerate payoff function.17 C.Fashion Leaders We now consider a scenario in which individuals have different signal precisions(accuracy).In particular,consider the binary signal case of table 1,where higher precision of individual i's signal refers to a higher value ofp We assume that Pr(V=1)=Pr(V=0)=1. RESULT 1.Suppose that the binary signal case obtains.(1)If C= and if the individual with the highest precision decides first,then the first individual's decision is followed by all later individuals. (2)Assume that all individuals n 1 observe signals of identical precision.Then all individuals n>2 are better off if the first individ- ual's precision is slightly lower rather than slightly higher than theirs. Proof.(1)The second individual infers the first individual's signal and so ignores his own information,starting a cascade.(2)If the first individual's precision is slightly higher,the second individual defers to the first individual;if it is slightly lower,the second individual makes his own decision.Thus the latter case leads to more informa- tion for later individuals.Q.E.D. Result 1 illustrates that small differences in precision can be very important and can lead to cascades that are even less informative (and,so,potentially even more fragile)than when individuals have identically distributed signals.While order is exogenous in the model, it is plausible that the highest-precision individual decides first.Con- sider a more general setting in which all individuals have the choice to decide or to delay,but there is a cost of delaying decision.All individuals have an incentive to wait in the hope of free-riding on the first to decide.However,other things equal,the cost of deciding early is lowest for the individual with the highest precision. The fashion leader model applies to situations in which a veteran performs a task with novices.If an experienced individual acts first, others frequently imitate.The prediction that a low-precision individ- ual imitates a higher-precision predecessor is consistent with the evi- dence of numerous psychological experiments demonstrating that a subject's previous failure in a task raises the probability that in further 17 As Lee(1991)shows,with a continuum of actions,behavior generically converges to the correct action
INFORMATIONAL CASCADES 1003 trials he will imitate a model performing the task(see Thelen,Dol- linger,and Kirkland 1979,p.146).Deutsch and Gerard(1955)also give experimental evidence that the more uncertain an individual is about the correctness of his judgment,the more susceptible he is to informational influences on his decisions.Being better informed, teachers and parents are natural opinion leaders(see Ainlay,Becker, and Coleman 1986).Rogers(1983)summarizes studies that show that community leaders have superior information.18 Similarly,Stamps (1988,p.340)summarizes evidence that among territorial animals, "individuals acquiring their first territory in an unfamiliar habitat are more apt to prefer territories next to previous settlers than would territory owners or floaters that had lived in the habitat in the past." Result 1 illustrates that a very slight perturbation in the informa- tional setting may make a very large difference(between an immedi- ate or later cascade).Thus to understand the "cause"of a social change,it is crucial to pay careful attention to the early leaders.In- deed,when mass behavior arises idiosyncratically from chance early events,it can be futile to seek grand causal forces. Result I also suggests that an individual who wishes to bring about a social change,for example,introduce a desirable innovation such as an improved sanitary method in a peasant community,must focus his efforts on persuading early community leaders.Assume,for ex- ample,that individuals are ordered by precisions.Suppose that the "change agent"can persuade by causing one individual's signal real- ization to be(correctly)high,that is,perfect information precision. Suppose,however,that others are not aware of the improved preci- sion of the persuaded individual.Then the change agent should focus his efforts on the first and best-informed individual.Studies by Bliss (1952,p.30)and Alers-Montalvo (1957,p.6)find that individuals attempting to bring about social change are more successful when they work through community leaders (who tend to be better in- formed).19 Although we have suggested that higher-precision individuals tend to decide earlier,it is worth considering what occurs if a higher- 18 Rogers and van Es(1964)provide evidence that community leaders in Colombian peasant communities have more formal education,higher literacy,larger farms,higher social status,more exposure to mass media,and more political knowledge than follow- ers(see also Rogers and Shoemaker 1971).Some social psychologists have recognized that imitation may be based on a belief that high-prestige individuals are good decision makers.Bandura(1977,p.89)states that "in situations in which people are uncertain about the wisdom of modeled courses of action,they must rely on such cues as general appearances,speech,style,age,symbols of socioeconomic success,and signs of exper- tise as indicators of past successes." Our prediction that the first individual is enirely decisive is often unrealistic.A milder result,that the first individual is disproportionately influential,could be derived under a more general information structure