Detection of Non-self-correcting Nature of Information Cascade

Abstract

We propose a method of detecting non-self-correcting information cascades in experiments in which subjects choose an option sequentially by observing the choices of previous subjects. The method uses the correlation function C(t) between the first and the $t+1$th subject’s choices. C(t) measures the strength of the domino effect, and the limit value $c\equiv \lim _{t\rightarrow \infty }C(t)$ determines whether the domino effect lasts forever $(c>0)$ or not $(c=0)$. The condition $c>0$ is an adequate condition for a non-self-correcting system, and the probability that the majority’s choice remains wrong in the limit $t\rightarrow \infty$ is positive. We apply the method to data from two experiments in which T subjects answered two-choice questions: (i) general knowledge questions ($T_{avg}=60$) and (ii) urn-choice questions ($T=63$). We find $c>0$ for difficult questions in (i) and all cases in (ii), and the systems are not self-correcting.