Date: 2025-05-27
Designer: Hiro KATAOKA (University of Tsukuba)
Hypotheses: Echo chambers are observed if beliefs evolve independently of opinions
100 agents; 1 runs; 3000 games
fixed variables: EPSILON WORKFLOW TOPIC ATOM PACTIVE PREWRITE NBITERATIONS NBAGENTS NBRUNS ALPHA MU REWRITE VALUE PREHOC OPDISTWEIGHT ACCEPTANCE_DESCISION ORDER
controled variables: DELTAS SEEDS
dependent variables: eb
Before verifying each hypotheses, we define the measures needed to check them. Let $A$ be the set of agents. Let $\mathcal S^t$ be the set of strongly connected components of the network of agents at time $t$. Let $T$ be the number of iterations (3000).
This measure counts the ratio of communities (i.e., strongly connected components) such that:
to all of the communities, where
$$ L^t(C)=\frac{|\{(a,a')\in N^t;a\in C\land a'\notin C\}|}{|\{(a,a')\in N^t;a\in C\}|}, $$
$$ M_B^t(C) = \max_{a,a'\in C}d_B(B_a^t,B_{a'}^t) $$
and
$$ D_B^t(C)=\forall s\in [t_C,T),M_B^s(C)\geq M_B^{s+1}(C). $$
Here, $d_B$ is the Hamming distance over the models of two beliefs:
$$ d_B(B,B')=|\mathcal M(B)\setminus\mathcal M(B')|+|\mathcal M(B')\setminus\mathcal M(B)|. $$
More formally, $eb$ is defined as:
$$ eb^t=|\{C\in\mathcal S^t;L^t(C)\leq 0.5\land M_B^t(C)=0\land D_B^t(C)\}| $$
In complement, we compute the proportion of agents involved in echo chambers.
Date: 2025-05-27
Performer: Hiro KATAOKA (University of Tsukuba)
The whole experiment, from scratch, can be executed through:
Hardware: AMD EPYC 7302P (16) @ 3.000GHz, Memory 128GB
OS: Ubuntu 22.04.5 LTS x86_64
Nim version: 2.2.0
Simulator version: ca6b226c686026a0d615dd968fae0b25a0017a5d
Before computing the measures, we test whether agents' beliefs and the network they form are stable. We regard them as stable iff they do not change during the last 20 interactions: $\forall t\in [T-20,T],\forall a\in A,B_a^t\equiv B_a^T$ for beliefs and $\forall t\in [T-20,T],\mathcal S^t=\mathcal S^T$ for the network. This means that agents do not change their beliefs and neighbors during the last 10 times (in expectation) they are active.
The table above shows the distribution of the minimal time $T'$ such that $\forall t\in [T',T],\forall a\in A,B_a^t\equiv B_a^T$. It shows that for all experiments $T'<T-20$. Thus, beliefs are stable.
The table above shows the distribution of the minimal time $T'$ such that $\forall t\in [T',T],\forall a\in A,\mathcal S^t=\mathcal S^T$. It shows that for all experiments $T'<T-20$. Thus, the network is stable.
Since everything is stable, now we compute the measures.
The table below shows some statistics of $eb^T$, the number of agents in beliefs echo chambers (agents_eb), $|\mathcal S^T|$, and the number of singletons (i.e., $|\{C\in\mathcal S^t;|C|=1\}|$).
From this table, in all of the experiments, $eb^T>0$.
The table below shows the list of experiments which end with $eb^T=1$.
The experiment 4-103848 is the only one experiment such that $|\mathcal S^T|=1$.
The final networks of these experiments listed above colored with agents' beliefs are as follows.
All agents share the same beliefs.
Next, we show the list of experiments with $eb^T=2$:
Different beliefs are shared in different echo chambers.
The network at $t=T$ is the same as it at $t=30$. From the evolutions, we could not see the two-step evolutions (i.e., split into some disconnected components and then segregation within each weakly connected components). However, when each beliefs echo chambers appear differs:
The correspondence between colors and beliefs is as follows:
In the network below, beliefs echo chambers are surrounded by solid lines; other components are surrounded by dashed lines.
The hypothesis is supported: we can always observe beliefs echo chambers.
This file can be retrieved from URL https://sake.re/20250528-BROD
