998 JOURNAL OF POLITICAL ECONOMY noisy signal,as whenp=+e,with e arbitrarily small,this probabil- ity after only 10 individuals is less than 0.1 percent! We can also derive the probability of ending up in the correct cascade.The probabilities of an Up cascade,no cascade,or a DowN cascade after two individuals,given that the true value is one,are 中+1) 2p1-, 中-2)中-1) 2 (2) and after an even number of individuals n are 中+1[1-（中-2）2] ，（中-2）2， 2(1-p+2) (中-2)（中-1）[1-（中-2）2] (3) 2(1-p+2) The first expression is the probability of the correct cascade.It can be shown that this probability is increasing in p(see fig.1)and n.Even for very informative signals(where p is far from )the probability of the wrong cascade is remarkably high. The problem with cascades is that they prevent the aggregation of information of numerous individuals.Ideally,if the information of many previous individuals is aggregated,later individuals should con- verge to the correct action.However,once a cascade has started, Prob 1.0 Correct Cascade 0.8 0.6 .41 2 Incorrect Cascade 0.60.70.80.91.0 Signal Accuracy (p) FIc.1.-Probability of a correct and an incorrect cascade as a function ofp(p is the probability that the signal is high [H]given that the true value is high [eq.(1)1).Even for large p,the probability of ending up in the wrong cascade is considerable