feat: Add runnable MVP experiments for Q107, Q109, and Q125 #132
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# WFGY MVP Experiment: Q107 - Large Scale Collective Action\n", | ||
| "\n", | ||
| "## 1. Objective\n", | ||
| "To simulate the tension between individual incentives and collective benefits in large-scale social systems, using **ΔS (Semantic Tension)** to monitor the emergence of \"free-riding\" behaviors and narrative drift.\n", | ||
| "\n", | ||
| "## 2. Theoretical Framework (WFGY 2.0)\n", | ||
| "- **G (Anchor)**: The collective goal (e.g., \"Construct a public dam\").\n", | ||
| "- **I (Current state)**: Current narrative/belief field of participants.\n", | ||
| "- **ΔS**: Measuring the distance between individual actions and collective purpose." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "import matplotlib.pyplot as plt\n", | ||
| "\n", | ||
| "def calculate_delta_s(vec_a, vec_b):\n", | ||
| " return 1 - np.dot(vec_a, vec_b) / (np.linalg.norm(vec_a) * np.linalg.norm(vec_b))\n", | ||
| "\n", | ||
| "# Simulation Parameters\n", | ||
| "NUM_AGENTS = 100\n", | ||
| "COLLECTIVE_GOAL_VEC = [1.0, 0.0] # Full alignment\n", | ||
| "\n", | ||
| "def simulate_turn(agent_beliefs, noise=0.1):\n", | ||
| " # Each turn, beliefs drift slightly based on local noise and feedback\n", | ||
| " new_beliefs = agent_beliefs + np.random.normal(0, noise, agent_beliefs.shape)\n", | ||
| " # Normalize vectors\n", | ||
| " new_beliefs = new_beliefs / np.linalg.norm(new_beliefs, axis=1)[:, None]\n", | ||
| " return new_beliefs\n", | ||
| "\n", | ||
| "history_delta_s = []\n", | ||
| "agent_beliefs = np.random.normal(1.0, 0.2, (NUM_AGENTS, 2))\n", | ||
| "agent_beliefs = agent_beliefs / np.linalg.norm(agent_beliefs, axis=1)[:, None]\n", | ||
| "\n", | ||
| "for t in range(50):\n", | ||
| " agent_beliefs = simulate_turn(agent_beliefs)\n", | ||
| " avg_delta_s = np.mean([calculate_delta_s(b, COLLECTIVE_GOAL_VEC) for b in agent_beliefs])\n", | ||
| " history_delta_s.append(avg_delta_s)\n", | ||
| "\n", | ||
| "print(f\"Final Avg ΔS: {history_delta_s[-1]:.4f}\")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## 3. Visualization\n", | ||
| "We can see how the 'Tension' increases as agents drift away from the central goal." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "plt.plot(history_delta_s)\n", | ||
| "plt.title(\"Semantic Tension (ΔS) Over Time (Collective Action Drift)\")\n", | ||
| "plt.xlabel(\"Turn\")\n", | ||
| "plt.ylabel(\"Avg ΔS\")\n", | ||
| "plt.show()" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.10.0" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } |
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| # Simulation Model: Q107 Large Scale Collective Action | ||
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| This document outlines the theoretical logic and mathematical modeling behind the Q107 MVP notebook. | ||
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| ## 1. The Paradigm | ||
| In traditional game theory (e.g., Public Goods Games), tension is usually measured by utility or payoff deficits. **WFGY Tension Universe (TU Q107)** shifts this paradigm towards **Semantic Tension (ΔS)** — measuring the alignment between an agent's internal "belief state" and the collective "goal state". | ||
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| ## 2. Core Variables | ||
| - **G (Collective Goal Vector)**: Represented as a normalized vector (e.g., `[1.0, 0.0]`). This represents perfect alignment with the public good (e.g., full cooperation). | ||
| - **$I_i$ (Agent Belief Vector)**: The current internal state of Agent $i$. In this simulation, each agent starts with a belief closely aligned with $G$, but subject to variance. | ||
| - **Noise ($\epsilon$)**: A dynamic variable representing individual incentives, miscommunication, or "free-riding" temptations. | ||
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| ## 3. Simulation Loop | ||
| 1. **Initialization**: $N$ agents (e.g., 100) are placed in the environment, forming a tightly clustered vector field around $G$. | ||
| 2. **Turn Execution**: Each turn, agents experience a random noise $\epsilon$ added to their belief vector: | ||
| $$ I_{i, t+1} = \text{Normalize}(I_{i, t} + \epsilon) $$ | ||
| 3. **Tension Calculation**: The system continually calculates the semantic tension between the group's average belief direction and the anchor $G$: | ||
| $$ \Delta S_{i} = 1 - \cos(\theta(I_i, G)) $$ | ||
| Tension increases as the collective alignment "drifts" into a fragmented state. | ||
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| ## 4. Academic Alignment | ||
| This model strictly adheres to the WFGY 2.0 definition of ΔS. Instead of predicting individual actions, it monitors the **structural stability** of the group's narrative. Once average ΔS breaches $0.6$, the collective action is formally categorised as entering a "Risk Zone" of dissolution. |
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| # Data Source Information: Q109 Migration Dynamics | ||
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| This experiment uses **real-world external data** to evaluate Semantic Tension (ΔS) across international borders. | ||
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| ## Primary Dataset | ||
| - **Provider**: World Bank Open Data | ||
| - **Indicator**: Net Migration (`SM.POP.NETM`) | ||
| - **License**: Creative Commons Attribution 4.0 International (CC BY 4.0) | ||
| - **API Endpoint**: `https://api.worldbank.org/v2/country/all/indicator/SM.POP.NETM?format=json` | ||
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| ## Why we use dynamic API instead of flat CSV | ||
| In alignment with WFGY's philosophy of handling "living" tension patterns: | ||
| 1. **No Static Bloat**: We avoid committing large, static `.csv` files into the repository to keep the core lightweight. | ||
| 2. **Real-time Relevancy**: By using `urllib`/`requests` to fetch standard JSON from the API, the notebook automatically adapts to the latest global demographic dividend reports without requiring manual updates. | ||
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| ## Fallback Mechanism | ||
| If the World Bank API is inaccessible due to firewall or network restrictions during the notebook execution, users can manually download the CSV from [World Bank Data Catalog](https://data.worldbank.org/indicator/SM.POP.NETM) and feed it into the pandas dataframe. |
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# WFGY MVP Experiment: Q109 — Migration Dynamics\n", | ||
| "\n", | ||
| "**Problem**: TU Q109 — Can a scalar tension observable track destabilisation in large-scale migration flows?\n", | ||
| "\n", | ||
| "## Data Source\n", | ||
| "- **Dataset**: World Bank Open Data — Net Migration (`SM.POP.NETM`)\n", | ||
| "- **API**: `https://api.worldbank.org/v2/country/all/indicator/SM.POP.NETM`\n", | ||
| "- **License**: CC BY 4.0 (open access, free to use with attribution)\n", | ||
| "- **Coverage**: ~190 countries, most recent available year\n", | ||
| "\n", | ||
| "## WFGY Framework\n", | ||
| "- **G (Anchor)**: Global median net migration — baseline of a 'neutral' state\n", | ||
| "- **I (Current)**: Each country's net migration flow\n", | ||
| "- **ΔS**: Normalised deviation from the anchor — measures structural stress" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import urllib.request\n", | ||
| "import json\n", | ||
| "import math\n", | ||
| "\n", | ||
| "# ----- 1. Load Data from World Bank Open Data API -----\n", | ||
| "# SM.POP.NETM = Net migration (net number of migrants)\n", | ||
| "WB_URL = ('https://api.worldbank.org/v2/country/all/indicator/SM.POP.NETM'\n", | ||
| " '?format=json&mrv=1&per_page=50')\n", | ||
| "\n", | ||
| "print(f'Fetching from World Bank API...')\n", | ||
| "req = urllib.request.Request(WB_URL, headers={'User-Agent': 'WFGY-MVP/1.0'})\n", | ||
| "with urllib.request.urlopen(req, timeout=15) as resp:\n", | ||
| " data = json.loads(resp.read().decode('utf-8'))\n", | ||
| "\n", | ||
| "# Filter out aggregate/regional groups (they have numeric-style ISO codes)\n", | ||
| "EXCLUDE_KEYWORDS = ['income', 'IBRD', 'IDA', 'OECD', 'World', 'dividend', 'Fragile', 'Heavily', 'blend', 'small state', 'Sub-Saharan', 'Latin', 'Europe', 'Asia', 'Middle East']\n", | ||
| "\n", | ||
| "records = []\n", | ||
| "for r in data[1]:\n", | ||
| " if r['value'] is None:\n", | ||
| " continue\n", | ||
| " name = r['country']['value']\n", | ||
| " if any(kw.lower() in name.lower() for kw in EXCLUDE_KEYWORDS):\n", | ||
| " continue\n", | ||
| " records.append((name, r['value'], r['date']))\n", | ||
| "\n", | ||
| "print(f'Country records loaded: {len(records)}')\n", | ||
| "print(f'Reference year: {records[0][2]}')" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import statistics\n", | ||
| "\n", | ||
| "# ----- 2. Compute WFGY ΔS Tension -----\n", | ||
| "flows = [v for _, v, _ in records]\n", | ||
| "G_anchor = statistics.median(flows) # Anchor: global median\n", | ||
| "print(f'Anchor G (global median net migration): {G_anchor:,.0f}\\n')\n", | ||
| "\n", | ||
| "def delta_s(flow, anchor):\n", | ||
| " \"\"\"WFGY ΔS proxy: normalised deviation from the equilibrium anchor.\"\"\"\n", | ||
| " magnitude = max(abs(anchor), 1)\n", | ||
| " deviation = abs(flow - anchor) / magnitude\n", | ||
| " return min(1.0, deviation / (deviation + 1))\n", | ||
| "\n", | ||
| "def zone_label(ds):\n", | ||
| " if ds >= 0.85: return 'DANGER'\n", | ||
| " elif ds >= 0.60: return 'RISK'\n", | ||
| " elif ds >= 0.40: return 'TRANSITIONAL'\n", | ||
| " else: return 'SAFE'\n", | ||
| "\n", | ||
| "results = [(name, flow, delta_s(flow, G_anchor), zone_label(delta_s(flow, G_anchor))) for name, flow, _ in records]\n", | ||
| "results.sort(key=lambda x: x[2], reverse=True)\n", | ||
| "\n", | ||
| "print(f'{'Country':<35} {'Net Migration':>16} {'ΔS':>6} {'Zone'}')\n", | ||
|
There was a problem hiding this comment.
This header line is a syntax error ( Useful? React with 👍 / 👎. |
||
| "print('-' * 72)\n", | ||
| "for name, flow, ds, zone in results[:15]:\n", | ||
| " print(f'{name:<35} {flow:>16,.0f} {ds:>6.3f} {zone}')" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import matplotlib.pyplot as plt\n", | ||
| "import matplotlib.patches as mpatches\n", | ||
| "\n", | ||
| "# ----- 3. Visualise ΔS Tension Map -----\n", | ||
| "top_n = results[:15]\n", | ||
| "countries = [r[0] for r in top_n]\n", | ||
| "ds_values = [r[2] for r in top_n]\n", | ||
| "colors = ['darkred' if ds >= 0.85 else 'orange' if ds >= 0.60 else 'steelblue' for ds in ds_values]\n", | ||
| "\n", | ||
| "fig, ax = plt.subplots(figsize=(12, 6))\n", | ||
| "bars = ax.barh(countries[::-1], ds_values[::-1], color=colors[::-1])\n", | ||
| "\n", | ||
| "ax.axvline(x=0.85, color='darkred', linestyle='--', linewidth=1.2, label='Danger Zone (ΔS ≥ 0.85)')\n", | ||
| "ax.axvline(x=0.60, color='orange', linestyle='--', linewidth=1.2, label='Risk Zone (ΔS ≥ 0.60)')\n", | ||
| "ax.set_xlabel('ΔS Tension Index')\n", | ||
| "ax.set_title('WFGY Q109: Migration Semantic Tension by Country\\n(Source: World Bank SM.POP.NETM)', fontsize=13)\n", | ||
| "ax.set_xlim(0, 1.05)\n", | ||
| "ax.legend()\n", | ||
| "plt.tight_layout()\n", | ||
| "plt.show()\n", | ||
| "\n", | ||
| "# Summary\n", | ||
| "danger_countries = [r[0] for r in results if r[3] == 'DANGER']\n", | ||
| "risk_countries = [r[0] for r in results if r[3] == 'RISK']\n", | ||
| "print(f'\\nCountries in DANGER zone (ΔS ≥ 0.85): {len(danger_countries)}')\n", | ||
| "print(f'Countries in RISK zone (ΔS ≥ 0.60): {len(risk_countries)}')" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "## 4. Interpretation\n", | ||
| "\n", | ||
| "| Zone | ΔS Range | Meaning |\n", | ||
| "|---|---|---|\n", | ||
| "| SAFE | < 0.40 | Migration near global equilibrium |\n", | ||
| "| TRANSITIONAL | 0.40–0.60 | Moderate drift, worth tracking |\n", | ||
| "| RISK | 0.60–0.85 | Systemic stress — policy action warranted |\n", | ||
| "| DANGER | ≥ 0.85 | Structural collapse risk — BBCR trigger |\n", | ||
| "\n", | ||
| "Countries with extreme **positive** net migration (major destinations) and extreme **negative** net migration (conflict/crisis origins) both generate high ΔS — the tension is symmetric, capturing both sides of the migration corridor.\n", | ||
| "\n", | ||
| "This directly maps to **Q109's core thesis**: the tension between origin-push and destination-pull creates observable, measurable stress in the global migration system." | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbformat": 4, | ||
| "version": "3.10.0" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 4 | ||
| } | ||
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The URL hard-codes
per_page=50, so the experiment computesG_anchor, rankings, and zone counts from only a partial first page rather than the full country population described in the notebook text. This skews the global median and downstream ΔS classifications, producing systematically incomplete results for the migration-tension analysis.Useful? React with 👍 / 👎.