Date: 2025-01-14
Designer: Hiro KATAOKA (University of Tsukuba)
Hypotheses: Echo chambers are reinforced with opinions-beliefs interactions and fixed threshould for opinions
100 agents; 1 runs; 500 games
fixed variables: WORKFLOW TOPIC ATOM EPSILON PACTIVE PREWRITE NBITERATIONS NBAGENTS NBRUNS ALPHA MU REWRITE PREHOC
controled variables: DELTAS SEEDS INITS VALUES
dependent variables: mdo mdb ngo ngb ano anb
Before verifing each hypotheses, we define the measures needed to check them. These measures are the same as 20241209-BROD and 20241210-bROD.
This measure shows the maximal distance between opinions: $$ \max_{a,a'\in A}|O_a-O_{a'}| $$ or equivalently, $$ \max_a O_a - \min_{a'} O_{a'}. $$
Intuitively, the more mdo is, the more polarized agents' opinions are.
This measure shows the maximal distance between beliefs: $$ \max_{a,a'\in A}d(B_a,B_{a'}) $$ where $d$ is the Hamming distance between the sets of models $m$: $$ d(B,B')=|\{m;m\models B\oplus m\models B\}|, $$ with $\oplus$ as the exclusive or.
Intuitively, the more mdb is, the more polarized agents' beliefs are.
This measure shows the number of groups of agents based on opinions.
The $i$-th group $G_i$ is a nonempty subset of $A$ such that $G_i\cap G_j=\emptyset$ if $i\neq j$. Each $G_i$ can be defined by performing hierarchial clustering with complete linkage: two clusters $C$ and $C'$ are merged iff $$\max_{a\in C,a'\in C'}|O_a-O_{a'}|\leq 0.1$$
Intuitively, the more ngo is, the more polarized agents' opinions are.
This measure shows the number of groups of agents based on opinions.
The $i$-th group $G_i$ is a nonempty subset of $A$ such that $G_i\cap G_j=\emptyset$ if $i\neq j$. Each $G_i$ can be defined as the maximal subset of $A$ such that all members share the same beliefs, i.e., $$ \forall i,\forall a,a'\in G_i,B_a\equiv B_{a'}. $$ Or equivalently, this measure can be calculated by $|\{B_a;a\in A\}|$.
Intuitively, the more ngb is, the more polarized agents' beliefs are.
This measure shows the average number of neighbors in another communities. Let $G_1,\ldots,G_n$ be the groups based on opinions. Let $E(\subseteq A\times A)$ be the set of edges in the network agents form. Then, this measure is defined as follows: $$ \frac{1}{n}|\{(a,a')\in E; \exists ij.a\in G_i,a'\in G_j,i\neq j\}|. $$
Intuitively, the less ano is, the more segregated the network is.
This measure shows the average number of neighbors in another communities. Let $G_1,\ldots,G_n$ be the groups based on beliefs. Let $E(\subseteq A\times A)$ be the set of edges in the network agents form. Then, this measure is defined as follows: $$ \frac{1}{n}|\{(a,a')\in E; \exists ij.a\in G_i,a'\in G_j,i\neq j\}|. $$
Intuitively, the less anb is, the more segregated the network is.
Date: 2025-01-14
Performer: Hiro KATAOKA (University of Tsukuba)
The whole experiment, from scratch, can be executed through:
Hardware: AMD EPYC 7302P, Memory 128GB
OS: Ubuntu 22.04.5 LTS x86_64
Nim version: 2.2.0
Simulator version: 747763f895c41497a0f7066177762ba2d7cb93ff
To compare with the results from experiments with $\varepsilon=1.0$, we load the analyzed data from H1 (20241210-BROD):
We will use $0.01$ as the significance level.
First, we show the effect of $\delta$ on mdb.
For smaller $\delta$, the difference is small. For larger $\delta$, mdb is larger than the previous one.
With the Shapiro-Wilk test, the measure mdb from experiments for H1 and H2 follows a normal distribution because the $p$-values are lower than 0.01.
Thus we can perform paired $t$-test to see whether changing cultural values has an effect on mdb:
We see the significant difference between two experiments.
With the Shapiro-Wilk test, the measure mdb from experiments which share the same values follows a normal distribution because the $p$-values are lower than 0.01.
Thus we perform the paired $t$-test:
But we do not see the significance difference between them with respect to the significance level 0.01.
We test for each $\delta$:
mdb from experiments which share $\delta$ and the same cultural values follow normal distributions if $\delta\in\{2,5,7\}$. Thus, we perform the paired $t$-test for these $\delta$ and the Wilcoxon signed-rank test otherwise.
We perform the same analysis but always uses the Wilcoxon signed-rank test:
In both cases we do not see the significant difference.
ngb is always larger than it from previous experiment.
From the Shapiro-Wilk test, ngb from experiments for H1 and H2 follow normal distributions.
Thus we can perform the paired $t$-test:
We see the significant difference.
From the Shapiro-Wilk test, ngb from experiments which share the same cultural values follow normal distributions.
Thus we can perform the paired $t$-test:
The result shows that we do not see the significant difference.
Same analysis for each $\delta$:
From the table above which shows the results from the Shapiro-Wilk test, we use the paired $t$-test for $\delta\in\{4,5\}$ and the Wilcoxon signed-rank test otherwise.
The same analysis but always uses the Wilcoxon signed-rank test:
These tables show that we cannot observe the significant difference.
Excluding data from experiments which end with a single community yields the plot below:
Here, anb is always lower on average than it from the experiments for H1.
From the Shapiro-Wilk test, anb from the experiments for H1 and H2 follows normal distributions.
Thus we can perform the paired $t$-test:
We see the significant difference.
From the Shapiro-Wilk test, anb from the experiments which share the same cultural values follows normal distributions.
Thus we can perform the paired $t$-test:
Thus we cannot conclue that changing value has an effect on anb.
Next we perform the same analysis for $\delta$-wise:
From the table above, we use the paired $t$-test for $\delta\in\{5,6,7\}$ and the Wilcoxon signed-rank test otherwise:
The same analysis but always uses the Wilcoxon signed-rank test yields the following table:
In both cases we cannot conclude that changing values has the significant effect on anb in general. We can observe the effect only if $\delta=1$.
This file can be retrieved from URL https://sake.re/20241212-BROD