Experiment 20260122-BROD¶

Note. It has been found that the code implementing rewiring was not taking into account the current opinions and beliefs but those at the beginning of the workflow instead. Although this does not impact the main results of the notebook, the data is not reliable anymore. Such implementation has been corrected (see the corresponding commit).

Experiment design¶

Date: 2026-02-01

Designer: Hiro KATAOKA (University of Tsukuba)

Hypotheses: Minimal-oriented rewirings (with different definitions) allow agents to form less echo chambers than random/maximal-oriented rewirings

100 agents; 5000 games

Note: this experiment is a complement one to 20260121-BROD based on the correct parameter configurations for the minimal-oriented rewirings.

Variables¶

fixed variables: WORKFLOW TOPIC ATOM PACTIVE PREWRITE NBITERATIONS NBAGENTS NBRUNS ALPHA MU VALUE PREHOC

controlled variables: EPSILONS DELTAS SEEDS REWIRINGS

dependent variables: eo eb po pb uo ub

Values¶

This experiment is a complement to 20260120-BROD and 20250121-BROD: the minimal-oriented rewiring algorithms (but the different definitions) are considered here.

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 $t$.

eo (Opinion echo chamber)¶

This measure counts the number 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., $M_O^t(C)\leq 10^{-4}$;
• opinions have been reinforced, i.e., $D_O^t(C)$

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:

$$ eo^t=|\{C\in\mathcal S^t;L^t(C)\leq 0.5\land M_O^t(C)\leq 10^{-4}\land D_O^t(C)\}| $$

This measure is the same as what is used in [20250414-BROD].

eb (Belief echo chamber)¶

This measure counts the number 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., $M_B^t(C)=0$;
• opinions have been reinforced, i.e., $D_B^t(C)$

to all of the communities, where

$$ M_B^t(C) = \max_{a,a'\in C}d_B(B_a^t,B_{a'}^t) $$

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:

$$ eb=|\{C\in\mathcal S^t;L^t(C)\leq 0.5\land M_B^t(C)=0\land D_B^t(C)\}| $$

This measure is the same as what is used in [20250414-BROD].

po/pb (Population in opinion/belief echo chambers)¶

These measure count how many agents are in opinion/belief echo chambers, respectively.

uo (Unique opinions shared within opinion echo chambers)¶

This measure counts how many opinions are shared within opinion echo chambers. Let $A_O\subseteq A$ be the set of agents in opinion echo chambers. Then, this measure (roughly) returns $|\{O_a;a\in A_O\}|$.

To avoid applying strict equivalence check, i.e., $=$, toward several float numbers, we apply the hierarchical clustering with the allowed maximal distance $10^{-4}$.

ub (Unique beliefs shared within belief echo chambers)¶

This measure counts how many beliefs are shared within belief echo chambers. Let $A_B\subseteq A$ be the set of agents in belief echo chambers. Then, this measure returns $|\{B_a;a\in A_B\}|$.

Experiment¶

Date: 2026-02-01

Performer: Hiro KATAOKA (University of Tsukuba)

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

Parameter file: params.sh

Executed command (scipt.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: 4f849881931920f2fe1e4c83a1f1db8f0a8a1e20

Duration and Output¶

• Duration: 7 hours and 23 minutes
• Output: 52 GB

Raw Results¶

Raw results are available at Zenodo:

Analysis¶

We will use 0.01 for the significance threshold for the statistical tests.

Computing the measures¶

First, we compute the measures.

In the following analysis,

• results from the experiments with minob/minbo are based on what is referred from this notebook;
• results with other rewirings are taken from 20260120-BROD.

Note that the same measures are used for the two experiments.