WFGY/TensionUniverse/Experiments/Q108_MVP/README.md

TU Q108 MVP: toy political polarization

Status: Experiment A implemented and reproducible. Experiment B planned.

This page contains the first effective layer MVPs for TU Q108.
The goal is to make polarization tension visible in small, fully inspectable models.

Navigation

• ← Back to Experiments index
• ← Back to Event Horizon (WFGY 3.0)

---

0. What this page is about

TU Q108 looks at political polarization.

Instead of full media ecosystems, we use:

• opinion dynamics on simple graphs,
• modeled exposure to messages,
• and basic update rules that can be inspected line by line.

The MVP experiments define observables that track:

• clustering of opinions,
• distance between groups,
• and mismatch with declared goals like "pluralistic but not polarized".

Experiment A is implemented and runnable.
Experiment B is a planned extension for information filter design.

---

1. Experiment A: bounded confidence on different networks

1.1 Question

Can a single bounded confidence model, with the same people and the same update rule, behave very differently only because of network structure?

In other words:

• if we fix the initial opinions and the bounded confidence rule,

• and only change the social graph,

• can a scalar observable T_polar clearly separate:

  • a world that de-polarizes into a shared center, from
  • a world that stays locked in two opposing camps.

1.2 Model setup

Experiment A uses a deliberately simple toy world.

Agents

• N = 200 agents.
• Each agent holds a scalar opinion x in the range [-1, 1].

Initial opinions (two mild camps)

• Population is split into two labels: group 0 and group 1.
• Group 0 starts near -0.25 (normal noise, then clipped).
• Group 1 starts near +0.25 (same noise, same clipping).
• So the world begins with a mild left / right split, not full extremes.

Networks

We build two social graphs over the same agents:

1. well_mixed

   • Erdos–Renyi random graph with edge probability about 0.20.
   • Edges ignore the group labels.
   • Intuition: everyone mixes reasonably freely.

2. two_communities

   • Stochastic block model with two communities.
   • High internal linking probability (p_in ≈ 0.40).
   • Very low cross–community probability (p_out ≈ 0.01).
   • Intuition: two tightly knit echo chambers with few bridges.

Every other setting is identical between the two worlds.

Bounded confidence dynamics

Time is discrete, t = 0, 1, …, T.

• At each step, for each agent i:

  1. Pick a random neighbor j on the graph (if any).

  2. If the opinion distance |x_j − x_i| is less than or equal to epsilon:

     • move x_i towards x_j by a factor mu.

• Update is asynchronous: agents are visited in random order.

• Parameters in this MVP:

  • T_steps = 120 time steps,
  • mu = 0.5 (halfway step towards the neighbor),
  • epsilons explored: 0.15, 0.25, 0.35, 0.60.

Polarization observable T_polar

We partition agents into three groups, using a fixed center threshold:

• left group: opinion < -center_thresh,
• center group: absolute opinion <= center_thresh,
• right group: opinion > center_thresh,

where center_thresh = 0.15 in this MVP.

From this partition we compute:

• p_L: fraction of agents in the left group,
• p_C: fraction of agents in the center,
• p_R: fraction of agents in the right group,
• mu_L: mean opinion in the left group (if non-empty),
• mu_R: mean opinion in the right group (if non-empty),
• gap = absolute difference between mu_R and mu_L.

The scalar polarization tension T_polar is then constructed as

• T_raw = (p_L + p_R) * gap * (1 − p_C),
• T_polar is T_raw capped into the range [0, 1].

Interpretation:

• T_polar is large when

  • many agents sit in the extremes (large p_L + p_R),
  • the two camps are far apart (large gap),
  • the center is small (small p_C).

• T_polar is close to zero when

  • most agents sit near the center,
  • any remaining extremes carry little mass or little separation.

For diagnostics we also store:

• p_center_final = p_C,
• p_extreme_final = p_L + p_R.

1.3 Colab notebook (one-click run)

The Experiment A notebook is a single cell script, fully offline, designed for a one-click run.

The notebook will:

1. Build both networks (well_mixed and two_communities).

2. Initialize opinions with the same two-camp configuration.

3. Run bounded confidence dynamics for each epsilon and each network.

4. Compute T_polar, p_center_final, and p_extreme_final for every run.

5. Save all raw results to:

   • Q108_A_results.csv

6. Generate two PNG figures:

   • Q108_A_polarization_vs_epsilon.png
   • Q108_A_opinion_distributions_examples.png

No API key is required. All randomness is seeded for reproducibility.

1.4 Results

1.4.1 Summary table

The table below shows the aggregated statistics (mean over runs) for each network and epsilon.
T_polar_final_mean is the mean final T_polar. p_center_mean and p_extreme_mean are mean center and extreme fractions.

network_type	epsilon	T_polar_final_mean	p_center_mean	p_extreme_mean
two_communities	0.15	0.4712	0.037	0.963
two_communities	0.25	0.5122	0.003	0.997
two_communities	0.35	0.5016	0.000	1.000
two_communities	0.60	0.0000	1.000	0.000
well_mixed	0.15	0.4786	0.051	0.949
well_mixed	0.25	0.4895	0.040	0.960
well_mixed	0.35	0.0508	0.895	0.105
well_mixed	0.60	0.0000	1.000	0.000

Key observations:

• At epsilon 0.15 and 0.25, both networks stay in a strongly polarized regime.

  • T_polar around 0.47–0.51.
  • Almost everyone in the extremes, with p_extreme near 0.95–1.00.

• At epsilon 0.35, the networks diverge dramatically:

  • well_mixed

    • T_polar drops to about 0.05.
    • Around 89.5 percent of agents return to the center (p_center ≈ 0.895).
    • Only about 10.5 percent remain in the extremes.

  • two_communities

    • T_polar remains near 0.50.
    • Center is essentially empty (p_center ≈ 0).
    • All agents stay in extremes (p_extreme = 1.0).

• At epsilon 0.60, both networks fully de-polarize:

  • T_polar returns to 0.
  • Everyone sits in the center.

This means that at epsilon 0.35 we have:

• same agents,
• same initial two-camp opinions,
• same bounded confidence rule,
• same epsilon value,

but the final tension differs by an order of magnitude solely because of network structure.

1.4.2 T_polar as a function of epsilon

The figure below plots T_polar_final_mean versus epsilon for both networks.

Reading the figure:

• For both networks, small epsilons around 0.15–0.25 keep the world in a high-tension state.

• As epsilon grows, the well_mixed network de-polarizes first.

  • T_polar collapses at epsilon 0.35.

• The two_communities network remains locked in a strongly polarized state until epsilon is extremely large.

  • Only when epsilon reaches 0.60 does it finally collapse into the center.

In the language of Tension Universe:

• epsilon is a control knob,
• network modularity decides how far that knob actually moves the world.

1.4.3 Opinion distributions at the critical point

The second figure shows final opinion histograms at epsilon 0.35 for both networks.

Interpretation:

• well_mixed, epsilon = 0.35

  • Almost everyone has moved into a sharp central peak near 0.
  • The histogram is a single narrow spike, matching p_center ≈ 0.895 and T_polar ≈ 0.05.

• two_communities, epsilon = 0.35

  • The population remains split into two distinct peaks near -0.25 and +0.25.
  • The center is empty, matching p_center ≈ 0 and T_polar ≈ 0.50.

This figure visualizes the "same rules, different graph" story:

• In a well mixed world, slightly expanding tolerance leads to a shared center.
• In a modular world, the same tolerance leaves everyone locked in two opposing camps.

1.5 Interpretation and limitations

What Experiment A shows

• 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.

• T_polar acts as an effective layer observable that:

  • distinguishes between high-tension and low-tension regimes, and
  • makes the effect of epsilon and modularity directly comparable.

At epsilon 0.35:

• well_mixed: low tension, center-heavy world,
• two_communities: high tension, fully polarized world.

This gives TU Q108 a concrete, runnable example of "same world description at the micro level, different effective universe at the tension level".

Limitations and next knobs

• The current experiment focuses on mild initial separation (±0.25). More extreme starting points could explore even higher tension regimes.
• Only two network families are used here. Additional topologies (lattices, hubs, random geometric graphs) would extend the coverage.
• T_polar uses one center threshold (0.15). Other thresholds or multi-peak metrics could refine the observable for more complex landscapes.
• Time series of T_polar are logged only for illustrative runs. A full time-resolved analysis is left for future iterations.

---

2. Experiment B: information filter design tension (planned)

Experiment B is not yet implemented. It will reuse the same base model and T_polar, but focus on information filters as interventions.

2.1 Question

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?

The intent is to represent:

• diversity-boosting feeds,
• similarity-boosting feeds,
• random or noise-injecting feeds,

and compare how they move T_polar over time relative to a neutral baseline.

2.2 Planned setup

Using the same kind of networks and opinion initialization as Experiment A, the planned notebook Q108_B.ipynb will:

• introduce feed filters that bias which neighbors or messages an agent sees,
• run the same bounded confidence dynamics under each filter,
• track T_polar(t) over time.

A candidate T_filter would be:

• T_filter = T_polar(filter) − T_polar(neutral),

optionally weighted by the stated design goal ("reduce polarization", "increase diversity", and so on).

High positive T_filter would indicate a design that secretly amplifies tension despite its stated goal.

2.3 Status

• Notebook not yet implemented.
• This section is a placeholder for future work once Q108_B is promoted to MVP.

---

3. How TU Q108 fits into Tension Universe

TU Q108 treats political polarization as a tension between:

• individual opinion dynamics,
• network structure and media filters,
• declared goals for pluralism.

Experiment A provides:

• a minimal but fully runnable world,
• a scalar tension observable (T_polar),
• and a clean contrast between "well mixed" and "modular" universes.

Experiment B will extend this by treating filter design itself as a source of tension.

For broader context:

• Experiments index
• Event Horizon (WFGY 3.0)

---

Charters and formal context

This page is written under:

• TU Effective Layer Charter
• TU Encoding and Fairness Charter
• TU Tension Scale Charter