Market Psychology

Twenty people choose in turn. Each has a private signal that is right 60% of the time and sees everyone before them. Once one choice leads by two, the rest copy it and ignore their own signal. In 10,000 runs the queue ends in the wrong choice 31% of the time. Had all twenty signals been pooled and counted, the majority would be right 76% of the time (ties counting as wrong). Everyone acted sensibly; the information was lost because only actions were seen.

• Cascades are fragile: a public piece of news can break one at once, which is why herds reverse so sharply.
• In the lab people follow their own signal more than the theory predicts, so real cascades form less often (Anderson & Holt 1997).
• In markets prices move as people trade, which weakens pure cascades; the model is a lens, not a description.

rng = np.random.default_rng(7)

def queue(n=20, q=0.6):                           # the right choice is 1; each private signal is right 60% of the time
    acts, lead = [], 0                            # lead = adopters minus rejecters seen so far
    for _ in range(n):
        signal = 1 if rng.random() < q else 0
        act = (1 if lead > 0 else 0) if abs(lead) >= 2 else signal   # two ahead: copy the crowd, ignore the signal
        acts.append(act); lead += 1 if act else -1
    return acts

wrong_cascade = np.mean([queue()[-1] == 0 for _ in range(10_000)])
pooled_right = np.mean(rng.binomial(20, 0.6, 10_000) > 10)   # if all 20 signals were shared and counted

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up.