Experiment 20250530-BROD¶

Experiment design¶

Date: 2025-05-27

Designer: Hiro KATAOKA (University of Tsukuba)

Hypotheses: More echo chambers are observed if opinions and beliefs evolve at the same time but without synchronizing each other (with different order from 20250529-BROD)

100 agents; 1 runs; 3000 games

Variables¶

fixed variables: WORKFLOW TOPIC ATOM PACTIVE PREWRITE NBITERATIONS NBAGENTS NBRUNS ALPHA MU REWRITE VALUE PREHOC OPDISTWEIGHT ACCEPTANCE_DESCISION ORDER

controled variables: EPSILONS DELTAS SEEDS

dependent variables: eo eb

Values¶

Measures¶

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).

eo (Opinions echo chamber)¶

This measure counts the ratio of communities (i.e., strongly connected components) such that:

• they are segregated, i.e., $L^t(C)\leq 0.5$;
• opinions are homogeneous, i.e., $M_O^t(C)\leq 10^{-3}$;
• opinions have been reinforced, i.e., $D_O^t(C)$

to all of the communities, where

$$ L^t(C)=\frac{|\{(a,a')\in N^t;a\in C\land a'\notin C\}|}{|\{(a,a')\in N^t;a\in C\}|}, $$

$$ M_O^t(C) = \max_{a,a'\in C}|O_a^t-O_{a'}^t| $$

and

$$ D_O^t(C)=\forall s\in [t_C,T),M_O^s(C)\geq M_O^{s+1}(C). $$

Here, $[t_C,T]$ is the maximal time window such that $\forall t\in[t_C,T]$, $C\in\mathcal S^t$ and $T$ is the number of iterations.

More formally, $eo$ is defined as:

$$ eo^t=|\{C\in\mathcal S^t;L^t(C)\leq 0.5\land M_O^t(C)\leq 10^{-3}\land D_O^t(C)\}|. $$

In complement, we compute the proportion of agents involved in echo chambers.

eb (Beliefs echo chamber)¶

This measure counts the ratio of communities (i.e., strongly connected components) such that:

• they are segregated, i.e., $L^t(C)\leq 0.5$;
• beliefs are homogeneous, i.e., $M_B^t(C)=0$ (or equivalently, $\forall a,a'\in C$, $B_a^t\equiv B_{a'}^t$);
• opinions have been reinforced, i.e., $D_B^t(C)$

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.

Experiment¶

Date: 2025-05-27

Performer: Hiro KATAOKA (University of Tsukuba)

The whole experiment, from scratch, can be executed through:

Parameter file: params.sh

Executed command (script.sh):

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

Duration and Output¶

• Duration: 5 hours and 45 minutes
• Output: 14 GB

Raw Results¶

Raw results are available at Zenodo:

Analysis¶

Stabilization check¶

Before computing the measures, we test whether agents' opinions, beliefs and the network they form are stable. We regard them as stable iff they do not change during the last 20 interactions: $\forall t\in [T-20,T]$, $\forall a\in A,|O_a^t-O_a^T|\leq 10^{-3}$ for opinions, $\forall a\in A,B_a^t\equiv B_a^T$ 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 opinions, beliefs, and neighbors during the last 10 times (in expectation) they are active.

Opinions¶

The table above shows the distribution of the minimal time $T'$ such that $\forall t\in [T',T],\forall a\in A,|O_a^t-O_a^T|\leq 10^{-3}$. It shows that for some experiments $T'\geq T-20$. Thus, in some experiments, opinions are not stable. Here is the list of such experiments:

In this experiment, opinions have been evolved as follows:

The following plot is a part of the plot above: it shows the region satisfying $2750\leq t\leq 3000$ and $0.475\leq\text{opinion}\leq 0.5$.

Some agents' opinions are constantly changing.

Beliefs¶

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 in some experiments $T'\geq T-20$, hence, some of them are not stable. The list of such experiments is:

This is the same as before.

Network¶

The table above shows the distribution of the minimal time $T'$ such that $\forall t\in [T',T],\forall a\in A,\mathcal S^t=\mathcal S^T$. Again, in some experiments, the network is not stable. The list of such experiments is the same as before:

Computing the measure¶

Agents' opinions, beliefs, and networks are stable except for 1 out of 1400. Now we compute the measures.