Phase transition of social learning collectives and "Echo chamber"

TL;DR

This paper analyzes how social learning agents in a restless multi-armed bandit model exhibit a phase transition leading to an echo chamber, where agents overly concentrate on a single good lever as observation probability increases.

Contribution

It introduces a phase transition framework for social learning dynamics, revealing conditions under which agents form echo chambers and the associated statistical properties.

Findings

System exhibits a phase transition at a critical observation probability p_c.

Variance of agents with good levers diverges or remains finite depending on p.

Echo chambers form when observation probability exceeds a threshold, reducing diversity.

Abstract

An "Echo chamber" is the state of social learning agents whose performances are deteriorated by excessive observation of others. We understand this to be the collective behavior of agents in a restless multi-armed bandit. The bandit has $M$ good levers and bad levers. A good lever changes to a bad one randomly with probability $q_{C}$ and a new good lever appears. $N$ agents exploit ones' lever if they know that it is a good one. Otherwise, they search for a good one by (i) random search (success probability $q_{I}$) and (ii) observe a good lever that is known by other agents (success probability $q_{O}$) with probability $1-p$ and $p$, respectively. The distribution of agents in good levers obeys the Yule distribution with power law exponent $1+\gamma$ in the limit $N,M\to \infty$ and $\gamma=1+\frac{(1-p)q_{I}}{pq_{O}}$. The expected value of the number of the agents with a good lever $N_{1}$ increases with $p$. The system shows a phase transition at $p_{c}=\frac{q_{I}}{q_{I}+q_{o}}$. For $p<p_{c}\,(>p_{c})$, the variance of $N_{1}$ per agent $\mbox{Var}(N_{1})/N$ is finite (diverges as $\propto N^{2-\gamma}$ with $N$). There is a threshold value $N_{s}$ for the system size that scales as $\ln N_{s} \propto 1/(\gamma-1)$. For $p>p_{c}$ and $N<N_{s}$, all agents tend to share only one good lever. $\mbox{E}(N_{1})$ decreases to zero as $p\to 1$, which is referred to as the "Echo chamber".