Experiment 20251230-BROD¶

Experiment design¶

Date: 2025-12-30

Designer: Hiro KATAOKA (University of Tsukuba)

Hypotheses: The conclusions of 202504{10,11,12,14}-BROD are preserved if echo chamber measures are applied for the last 25 interactions and aggregated

100 agents; 5000 games

Variables¶

fixed variables: TWWIDTH

controled variables: EPSILONS DELTAS SEEDS

dependent variables: meo meb

Values¶

Measures¶

Before verifing 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 $t$.

meo (Mean of opinions echo chamber)¶

This measure counts the average 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., $D_O^t(C)$

during the last 25 interactions, 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, $meo$ is defined as:

$$ meo = \frac{1}{W} \sum_{t=T-W+1}^T eo^t $$

where $W$ is 25 and

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

meb (Mean of beliefs echo chamber)¶

This measure counts the average 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, $meb$ is defined as:

$$ meb = \frac{1}{W} \sum_{t=T-W+1}^T eb^t $$

where $W$ is 25 and

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

Experiment¶

Date: 2025-12-30

Performer: Hiro KATAOKA (University of Tsukuba)

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

Parameter file: params.sh

Raw Results¶

Raw results are available at:

• 20250410-BROD
• 20250411-BROD
• 20250412-BROD
• 20250414-BROD

This notebook contains additional analysis of these results. No new experiment is needed. These results should be placed under the directory results10, results11, results12, and results14, respectively.

Analysis¶

Computing the measures¶

First, we compute the measures.

Note that the functions corresponding to them are not optimized: they just compute $eo$ and $eb$ for $W$ times. This makes the execution time much more longer (especially in 20250412-BROD and 20250414-BROD). It is highly recommended to use the function starts with parallel_ if your computer has enough cores to reproduce the csv files as quick as possible.

20250410-BROD¶

20250411-BROD¶

20250412-BROD¶