Experiment 20260209-BROD¶

Experiment design¶

Date: 2026-02-09

Designer: Hiro KATAOKA (University of Tsukuba)

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

100 agents; 1 runs; 2000 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 (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:

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

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., $D_B^t(C)$

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). The number of iterations and the time window for stability tests are shorter than the previous experiments (2000 and 25, respectively) to make the total duration shorter.

Experiment¶

Date: 2026-02-09

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: 3 hours and 9 minutes
• Output: 24 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., 2000).

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.