Experiment 20260217-BROD¶

Experiment design¶

Date: 2026-02-17

Designer: Hiro KATAOKA (University of Tsukuba)

Hypotheses: The overall reults are not changed if the concordant neighbors are evaluated just before rewiring with longer iterations

100 agents; 1 runs; 5000 games

Variables¶

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

controled variables: WORKFLOWS EPSILONS DELTAS SEEDS

dependent variables: eo eb

Values¶

Measures¶

Before testing each hypothesis, 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 (Opinions 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:

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

eb (Beliefs 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., $D_B^t(C)$

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:

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

Note¶

This experiment is:

• a replacement of [20250410-BROD], [20250411-BROD], [20250412-BROD], and [20250414-BROD] with a bug fix of the simulator (commit to fix this);
• a replacement of [20260209-BROD] with longer iterations (5000 here).

Experiment¶

Date: 2026-02-17

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: 539b17d5e33cd29eba73fa76eab6c5ee9daac0f3

Duration and Output¶

• Duration: 7 hours and 40 minutes
• Output: 58 GB

Raw Results¶

Raw results are available at Zenodo:

Analysis¶

Let $A$ be the set of agents. Let $T$ be the number of iterations (i.e., 5000).

We use 0.01 for the significance threshold for statistical tests (Welch's $t$-test).

Computing the measures¶

First, we compute the measures listed above.