arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1607.01944physics.soc-phcond-mat.stat-mech
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社会学习集体的相变与“回音室”

Phase transition of social learning collectives and "Echo chamber"

Shintaro Mori, Kazuaki Nakayama, Masato Hisakado

摘要:

“回音室”是社会学习主体的状态,其表现因过度观察他人而恶化。我们理解这是一个不安分的多臂强盗中代理人的集体行为。强盗有$M$好杠杆和坏杠杆。一个好的杠杆以概率$q_{C}$随机地变成一个坏的杠杆,并且出现一个新的好杠杆。$N$代理人利用一个人的杠杆,如果他们知道这是一个好杠杆。否则,它们通过(i)随机搜索(成功概率$q_{I}$)和(ii)观察其他代理分别以概率$1-p$和$p$已知的好杠杆(成功概率$q_{O}$)来搜索好杠杆。在$N,M\to \infty$和$γ=1+\frac{(1-p)q_{I}}{pq_{O}}$的极限下,好杠杆中的代理分布服从具有幂律指数$1+γ$的Yule分布。具有良好水平$N_{1}$的代理数量的期望值随着$p$而增加。系统在$p_{c}=\frac{q_{I}}{q_{I}+q_{o}}$处显示出相变。对于$p<p_{c}\,(>p_{c})$,每种药物$\mbox{Var}(N_{1})/N$的$N_{1}$的方差是有限的(随着$\propto N^{2-γ}$与$N$的不同而不同)。系统大小有一个阈值$N_{s}$,按$\ln N_{s} \propto 1/(γ-1)$缩放。对于$p>p_{c}$和$N<N_{s}$,所有代理人往往只共享一个好杠杆。$\mbox{E}(N_{1})$作为$p\to 1$降低到零,这被称为“回声室”。

英文摘要:

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 $1+γ$ in the limit $N,M\to \infty$ and $γ=1+\frac{(1-p)q_{I}}{pq_{O}}$. 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 $\propto N^{2-γ}$ with $N$). There is a threshold value $N_{s}$ for the system size that scales as $\ln N_{s} \propto 1/(γ-1)$. 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".

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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