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@ -14,10 +14,10 @@ Use: When a user asks about TU Q108 polarization experiments or wants
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# TU Q108 MVP: toy political polarization
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_Status: work in progress. This page records early MVP designs and will be refined as the TU Q108 program matures._
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_Status: Experiment A implemented and reproducible. Experiment B planned._
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> This page sketches small opinion dynamics experiments for TU Q108.
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> The aim is to make polarization tension visible in simple, inspectable models.
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> This page contains the first effective layer MVPs for TU Q108.
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> The goal is to make polarization tension visible in small, fully inspectable models.
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**Navigation**
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@ -30,11 +30,11 @@ _Status: work in progress. This page records early MVP designs and will be refin
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TU Q108 looks at political polarization.
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Instead of real media ecosystems we work with:
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Instead of full media ecosystems, we use:
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- opinion dynamics on simple graphs,
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- modeled exposure to messages,
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- and basic update rules.
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- and basic update rules that can be inspected line by line.
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The MVP experiments define observables that track:
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@ -42,96 +42,308 @@ The MVP experiments define observables that track:
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- distance between groups,
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- and mismatch with declared goals like "pluralistic but not polarized".
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Experiment A is implemented and runnable.
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Experiment B is a planned extension for information filter design.
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---
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## 1. Experiment A: bounded confidence opinion dynamics
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## 1. Experiment A: bounded confidence on different networks
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### 1.1 Research question
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### 1.1 Question
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In a bounded confidence model, can we define a scalar observable T_polar that
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Can a single bounded confidence model, with the same people and the same update rule, behave very differently **only** because of network structure?
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- is small when opinions remain unimodal or gently clustered,
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- grows when bimodal or highly separated clusters form.
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In other words:
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### 1.2 Setup
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- if we fix the initial opinions and the bounded confidence rule,
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- and only change the social graph,
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- can a scalar observable T_polar clearly separate:
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- a world that de-polarizes into a shared center, from
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- a world that stays locked in two opposing camps.
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### 1.2 Model setup
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Experiment A uses a deliberately simple toy world.
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**Agents**
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- N = 200 agents.
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- Each agent holds a scalar opinion x in the range [-1, 1].
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**Initial opinions (two mild camps)**
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- Population is split into two labels: group 0 and group 1.
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- Group 0 starts near -0.25 (normal noise, then clipped).
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- Group 1 starts near +0.25 (same noise, same clipping).
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- So the world begins with a mild left / right split, not full extremes.
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**Networks**
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We build two social graphs over the same agents:
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1. `well_mixed`
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- Erdos–Renyi random graph with edge probability about 0.20.
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- Edges ignore the group labels.
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- Intuition: everyone mixes reasonably freely.
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2. `two_communities`
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- Stochastic block model with two communities.
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- High internal linking probability (p_in ≈ 0.40).
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- Very low cross–community probability (p_out ≈ 0.01).
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- Intuition: two tightly knit echo chambers with few bridges.
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Every other setting is identical between the two worlds.
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**Bounded confidence dynamics**
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Time is discrete, t = 0, 1, …, T.
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- At each step, for each agent i:
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1. Pick a random neighbor j on the graph (if any).
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2. If the opinion distance |x_j − x_i| is less than or equal to epsilon:
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- move x_i towards x_j by a factor mu.
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- Update is asynchronous: agents are visited in random order.
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- Parameters in this MVP:
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- T_steps = 120 time steps,
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- mu = 0.5 (halfway step towards the neighbor),
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- epsilons explored: 0.15, 0.25, 0.35, 0.60.
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**Polarization observable T_polar**
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We partition agents into three groups, using a fixed center threshold:
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- left group: opinion < -center_thresh,
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- center group: absolute opinion <= center_thresh,
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- right group: opinion > center_thresh,
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where center_thresh = 0.15 in this MVP.
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From this partition we compute:
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- p_L: fraction of agents in the left group,
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- p_C: fraction of agents in the center,
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- p_R: fraction of agents in the right group,
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- mu_L: mean opinion in the left group (if non-empty),
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- mu_R: mean opinion in the right group (if non-empty),
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- gap = absolute difference between mu_R and mu_L.
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The scalar polarization tension T_polar is then constructed as
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- T_raw = (p_L + p_R) * gap * (1 − p_C),
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- T_polar is T_raw capped into the range [0, 1].
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Interpretation:
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- T_polar is large when
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- many agents sit in the extremes (large p_L + p_R),
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- the two camps are far apart (large gap),
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- the center is small (small p_C).
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- T_polar is close to zero when
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- most agents sit near the center,
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- any remaining extremes carry little mass or little separation.
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For diagnostics we also store:
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- p_center_final = p_C,
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- p_extreme_final = p_L + p_R.
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### 1.3 Colab notebook (one-click run)
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The Experiment A notebook is a single cell script, fully offline, designed for a one-click run.
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[](https://colab.research.google.com/github/onestardao/WFGY/blob/main/TensionUniverse/Experiments/Q108_MVP/Q108_A.ipynb)
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The notebook will:
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- Place agents on a social network.
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- Assign each agent an initial opinion on a one dimensional scale.
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- Use a bounded confidence rule:
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1. Build both networks (`well_mixed` and `two_communities`).
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2. Initialize opinions with the same two-camp configuration.
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3. Run bounded confidence dynamics for each epsilon and each network.
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4. Compute T_polar, p_center_final, and p_extreme_final for every run.
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5. Save all raw results to:
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- agents only update toward neighbors whose opinions are within a threshold.
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- `Q108_A_results.csv`
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- Run dynamics for many timesteps under different thresholds and network structures.
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6. Generate two PNG figures:
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For each run compute:
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- `Q108_A_polarization_vs_epsilon.png`
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- `Q108_A_opinion_distributions_examples.png`
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- the distribution of opinions,
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- a polarization index based on cluster separation and within cluster variance,
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- a simple T_polar that increases with cluster separation and weight in extremes.
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No API key is required. All randomness is seeded for reproducibility.
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### 1.3 Expected pattern
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### 1.4 Results
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We expect:
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#### 1.4.1 Summary table
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- low T_polar when confidence bounds are wide and mixing is strong,
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- higher T_polar when narrow confidence and clustered connectivity drive separation.
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The table below shows the aggregated statistics (mean over runs) for each network and epsilon.
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T_polar_final_mean is the mean final T_polar. p_center_mean and p_extreme_mean are mean center and extreme fractions.
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Plots of trajectories and T_polar values will be added once implemented.
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| network_type | epsilon | T_polar_final_mean | p_center_mean | p_extreme_mean |
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|----------------|---------|--------------------|---------------|----------------|
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| two_communities | 0.15 | 0.4712 | 0.037 | 0.963 |
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| two_communities | 0.25 | 0.5122 | 0.003 | 0.997 |
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| two_communities | 0.35 | 0.5016 | 0.000 | 1.000 |
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| two_communities | 0.60 | 0.0000 | 1.000 | 0.000 |
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| well_mixed | 0.15 | 0.4786 | 0.051 | 0.949 |
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| well_mixed | 0.25 | 0.4895 | 0.040 | 0.960 |
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| well_mixed | 0.35 | 0.0508 | 0.895 | 0.105 |
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| well_mixed | 0.60 | 0.0000 | 1.000 | 0.000 |
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### 1.4 How to reproduce
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Key observations:
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After `Q108_A.ipynb` is available:
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- At epsilon 0.15 and 0.25, both networks stay in a strongly polarized regime.
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1. Open the notebook.
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2. Inspect the opinion update rules and polarization index definition.
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3. Run simulations with different parameters.
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4. Compare T_polar across runs.
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- T_polar around 0.47–0.51.
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- Almost everyone in the extremes, with p_extreme near 0.95–1.00.
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- At epsilon 0.35, the networks diverge dramatically:
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- `well_mixed`
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- T_polar drops to about 0.05.
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- Around 89.5 percent of agents return to the center (p_center ≈ 0.895).
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- Only about 10.5 percent remain in the extremes.
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- `two_communities`
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- T_polar remains near 0.50.
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- Center is essentially empty (p_center ≈ 0).
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- All agents stay in extremes (p_extreme = 1.0).
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- At epsilon 0.60, both networks fully de-polarize:
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- T_polar returns to 0.
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- Everyone sits in the center.
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This means that at epsilon 0.35 we have:
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- same agents,
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- same initial two-camp opinions,
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- same bounded confidence rule,
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- same epsilon value,
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but the final tension differs by an order of magnitude solely because of network structure.
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#### 1.4.2 T_polar as a function of epsilon
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The figure below plots T_polar_final_mean versus epsilon for both networks.
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Reading the figure:
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- For both networks, small epsilons around 0.15–0.25 keep the world in a high-tension state.
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- As epsilon grows, the `well_mixed` network de-polarizes first.
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- T_polar collapses at epsilon 0.35.
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- The `two_communities` network remains locked in a strongly polarized state until epsilon is extremely large.
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- Only when epsilon reaches 0.60 does it finally collapse into the center.
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In the language of Tension Universe:
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- epsilon is a control knob,
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- network modularity decides how far that knob actually moves the world.
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#### 1.4.3 Opinion distributions at the critical point
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The second figure shows final opinion histograms at epsilon 0.35 for both networks.
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Interpretation:
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- `well_mixed, epsilon = 0.35`
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- Almost everyone has moved into a sharp central peak near 0.
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- The histogram is a single narrow spike, matching p_center ≈ 0.895 and T_polar ≈ 0.05.
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- `two_communities, epsilon = 0.35`
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- The population remains split into two distinct peaks near -0.25 and +0.25.
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- The center is empty, matching p_center ≈ 0 and T_polar ≈ 0.50.
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This figure visualizes the "same rules, different graph" story:
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- In a well mixed world, slightly expanding tolerance leads to a shared center.
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- In a modular world, the same tolerance leaves everyone locked in two opposing camps.
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### 1.5 Interpretation and limitations
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**What Experiment A shows**
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- A single bounded confidence model, with a fixed set of agents and initial opinions, can produce very different polarization patterns purely by changing network structure.
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- T_polar acts as an effective layer observable that:
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- distinguishes between high-tension and low-tension regimes, and
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- makes the effect of epsilon and modularity directly comparable.
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At epsilon 0.35:
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- well_mixed: low tension, center-heavy world,
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- two_communities: high tension, fully polarized world.
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This gives TU Q108 a concrete, runnable example of "same world description at the micro level, different effective universe at the tension level".
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**Limitations and next knobs**
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- The current experiment focuses on mild initial separation (±0.25). More extreme starting points could explore even higher tension regimes.
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- Only two network families are used here. Additional topologies (lattices, hubs, random geometric graphs) would extend the coverage.
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- T_polar uses one center threshold (0.15). Other thresholds or multi-peak metrics could refine the observable for more complex landscapes.
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- Time series of T_polar are logged only for illustrative runs. A full time-resolved analysis is left for future iterations.
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---
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## 2. Experiment B: information filter design tension
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## 2. Experiment B: information filter design tension (planned)
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### 2.1 Research question
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Experiment B is not yet implemented. It will reuse the same base model and T_polar, but focus on **information filters** as interventions.
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Can we treat different information filter designs as interventions and define a tension observable T_filter that captures when a design meant to reduce polarization actually increases it.
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### 2.1 Question
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### 2.2 Setup
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Given a social graph and initial opinions, can we treat content feed designs as separate "world builders" and define a tension observable T_filter that captures when a design meant to reduce polarization actually increases it?
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Using the same base model, the notebook will:
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The intent is to represent:
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- Implement content feed filters, such as:
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- diversity-boosting feeds,
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- similarity-boosting feeds,
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- random or noise-injecting feeds,
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- diversity boosting,
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- similarity boosting,
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- random mixing.
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and compare how they move T_polar over time relative to a neutral baseline.
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- Run simulations under each filter design.
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- Track changes in T_polar over time.
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### 2.2 Planned setup
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Define T_filter as:
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Using the same kind of networks and opinion initialization as Experiment A, the planned notebook `Q108_B.ipynb` will:
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- the difference between T_polar under a given filter and under a neutral baseline,
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- weighted by the stated goal of the filter (for example "reduce polarization").
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- introduce feed filters that bias which neighbors or messages an agent sees,
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- run the same bounded confidence dynamics under each filter,
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- track T_polar(t) over time.
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### 2.3 Expected pattern
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A candidate T_filter would be:
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We expect:
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- T_filter = T_polar(filter) − T_polar(neutral),
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- filters designed to mix opinions to have lower T_filter when they succeed,
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- cases where miscalibrated filters increase T_polar to have higher T_filter, exposing design tension.
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optionally weighted by the stated design goal ("reduce polarization", "increase diversity", and so on).
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### 2.4 How to reproduce
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High positive T_filter would indicate a design that secretly amplifies tension despite its stated goal.
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Once `Q108_B.ipynb` exists:
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### 2.3 Status
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- open and inspect the filter implementations,
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- run the simulation and compare T_filter across filter types.
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- Notebook not yet implemented.
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- This section is a placeholder for future work once Q108_B is promoted to MVP.
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---
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## 3. How this MVP fits into Tension Universe
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## 3. How TU Q108 fits into Tension Universe
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TU Q108 treats political polarization as a tension between:
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@ -139,14 +351,15 @@ TU Q108 treats political polarization as a tension between:
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- network structure and media filters,
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- declared goals for pluralism.
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This MVP offers:
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Experiment A provides:
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- a bounded confidence experiment with T_polar,
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- a filter design experiment with T_filter.
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- a minimal but fully runnable world,
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- a scalar tension observable (T_polar),
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- and a clean contrast between "well mixed" and "modular" universes.
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Both are toy but capture the basic tension geometry.
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Experiment B will extend this by treating filter design itself as a source of tension.
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For context:
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For broader context:
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- [Experiments index](../README.md)
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- [Event Horizon (WFGY 3.0)](../../EventHorizon/README.md)
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