Is the mean-field's overshoot on the ring crowd caused by finite-size noise or by memory correlation?

What it found

Three models of the ring walking-side game (N = 200, M = 9, ε = 0.02, 20 seeds) are compared on the smallest robot share that tips the crowd: the deterministic mean-field of society-ringmf, a noisy memoryless resampling variant, and the society-allies simulation. The simulation lies between the other two in 6 of 6 cells (spread robots at k = 2: 0.06 / 0.10 / 0.18), so noise lowers the threshold and memory persistence raises it. Limits: only 6 cells; the resampling model also changes update order, which is not separated from memory; thresholds ±0.02; M and ε are not sourced; 1D binary game.

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Robot societies among people

• Does a measured walking-side preference pin down how many robots tip a crowd's passing side?Fitting the stubborn-bloc model to the side preference Moussaïd et al. (2009) measured for two head-on walkers (about 17.5% left, read from their Fig. 4) puts the mean-field tipping robot share at 0.075 to 0.096 for memory 9 across error rates 0.02 to 0.30, against 0.217 for an unbiased crowd; memory matters more (0.033 to 0.053 at 5, 0.133 to 0.149 at 17) and a stubborn-right bloc raises it.
• Should a robot yield only to people in a hurry, or to everyone?Should a robot yield only to people in a hurry, or to everyone? With 30% robots and 20% urgent people, a fleet that yields only to the urgent cuts their cost by 40% (1.130 to 0.676) at a 3% cost to everyone else, is individually stable, and costs the robots 29%.
• How many robots does it take to change how a crowd walks?How many robots does it take to change which side a crowd walks on? Robots that hold a programmed side tip a crowd once they are 16–32% of it, more when people remember more past partners (simulation matches mean field within 0.02); just short of that they make people collide up to 14× as often as adaptive robots, and placement matters more than numbers when people meet only neighbours. Stylised.
• Do robots that keep to one side make people walk on it, or jam the corridor?Do robots that keep to one side make people walk on it, or jam the corridor? In a social-force corridor, robots that adapt change nothing, but robots that hold the left cut people's speed from 0.91 to 0.39 of desired by 30% of the crowd and halve lane separation, while people move to their side only gradually (no sharp tipping, unlike the 1D model). Stylised.
• Can a robot fleet's reputation survive one bad incident?Can a robot fleet's reputation survive one bad incident? In a model where trust spreads by experience and gossip, a dent always recovers because people keep meeting robots; reputation is lost only through avoidance (at a 0.30 avoid-below threshold, 20/20, 18/20 and 0/20 crowds recover under neutral, 2× and 4× negativity in gossip), and robots that explain failures recovered every time. Stylised.
• What does it cost robots to let people go first at a shared lift or narrow pavement?What does it cost robots to let people go first at a shared lift or narrow pavement? At load 0.9, deference cuts people's wait 6.5× (4.60 to 0.71) and raises robots' by 2.6 units; total waiting cost is conserved, so it pays only if a person's wait costs more than a robot's, and a lone defector waits far less (2.08 vs 7.65). Queueing model within 2.7% of closed forms.

All 31 Robot societies among people projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.