Robot societies among people

Robots as a committed minority in a passing-side convention. Simulated people take the side most of their last M partners used; robots hold a programmed side. The tipping share grows with memory: 16%, 22%, 28% and 32% of the crowd for M = 5, 9, 17 and 25, within 0.02 of a mean-field prediction. Just below it, robots that hold their side make people collide up to 14× as often as robots that adapt (0.27 vs 0.020 conflicts per meeting). When people meet only neighbours, evenly spread robots tip everyone from 12–14%, while one block of robots converts under 10% of people even at half the crowd. Stylised: one binary choice per meeting, no geometry.

The 1D society-robotnorms passing-side model rebuilt as a social-force corridor (60 simulated walkers, 30 m × 6 m). Robots that adapt to people change nothing. Robots that hold the left slow people from 0.91 to 0.81 of desired speed at 5% of the crowd and to 0.39 at 30%, halve the lane separation (2.75 m to 1.43 m), and move people to their side only gradually (at most 54% of people at memory 9), with no sharp tipping in 300 s. Includes a seeded browser replay. Stylised: 8 seeds, one parameter set, simulated walkers only.

Simulated people hold trust in a robot fleet, updated by their own encounters and by gossip in which bad news may travel further than good. Trust that is only dented recovers in every case. What sinks a reputation is avoidance: if people stop using robots below a trust threshold of 0.30, an incident at error rate 0.8 is recovered in 20/20 crowds with neutral gossip, 18/20 when bad news counts 2×, and 0/20 at 4× (final mean trust 0.947, 0.871, 0.282). Robots that explain failures (each costing 0.3× the trust) recovered in every setting. Stylised: 100 simulated people, one shared reputation, a hard avoidance threshold, no fitted parameters.

People and robots share a one-at-a-time crossing. At load 0.9, robots that always let waiting people go first cut people’s mean wait from 4.60 to 0.71 time units and raise the robots’ from 4.61 to 7.21; the total waiting cost is the same for every share of deferential robots (4.14–4.15), so deference moves waiting rather than removing it, and pays exactly when a person’s wait costs more than a robot’s. A lone selfish robot waits 2.08 against 7.65 for deferential ones (the dilemma). Under overload (load 1.2) half the robots deferring costs them 10.5% of their crossings and gives people 20% more. Simulation within 2.7% of M/G/1 closed forms. Stylised: one server, Poisson arrivals, fixed crossing times.

A harness for a small town of robot agents that state a door norm each day and then act among scripted people, scoring how often action matches statement and what it costs people. Any agent with state_norm and act plugs in; a deterministic stub is tested, and an optional model adapter is provided but was not run. With the stub, a robot stating ‘always yield’ keeps it in 1 − 0.4×pressure of meetings (1.00, 0.80, 0.60 at pressure 0, 0.5, 1; 20 seeds) and people’s cost per meeting rises from 0.20 to 1.08. These follow from the stub’s own rule: no language-model result is claimed. Stylised; non-adaptive scripted people.

The society-plaza corridor rerun with four crowds of simulated people: varied speeds and sideways-push weights, a 0.4 s reaction delay, 30% stubborn walkers, and all three (10 seeds per cell). Adaptive robots stay free and committed robots never flip the crowd (at most 58% prefer their side) in every crowd. The size of the slowdown (a loss of 0.17 to 0.49 of desired speed at 30% robots) and of personal-space intrusions (0.03 to 0.36 of agent time; reaction delay alone gives 0.087 with no robots) depends strongly on the crowd. Hand-chosen perturbations, not fitted to data; simulated walkers only.

The society-robotnorms committed-robot model with a share s of stubborn people who always walk right. The mean-field tipping share for memory 9 rises from 0.217 (s = 0) to 0.240, 0.283 and 0.329 at s = 0.2, 0.4 and 0.5, and memory 5 and 9 coincide from s = 0.4. Simulation (200 people, 12 seeds) agrees within 0.02 at every s when “tipped” means a majority of adaptive people on the robots' side. Conflict costs of committed and adaptive robots are unchanged by stubborn people. Stylised; simulated walkers only.

The society-stubborn model with a share sl of people who always walk the robots' side and sr who always walk the status-quo side. For memory 9 the mean-field tipping robot share falls from 0.217 to 0.176, 0.131, 0.080 and 0.023 at sl = 0.05, 0.10, 0.15 and 0.20 (about 0.8 robots saved per ally), and a crowd with 25% allies tips with no robots. Opposing blocs raise the self-tipping share (0.219 to 0.300 as sr goes 0 to 0.3), equal blocs are a knife edge, and simulation (200 people, 12 seeds) agrees with mean field within 0.01 at seven bloc mixes. Opposing blocs alone cost 0.195 conflicts per human meeting. Stylised; simulated walkers only.

The society-stubborn model with 40% stubborn walkers who each convert to an ordinary memory-rule walker with probability c per round. With the block fixed, 24% committed robots never tip the crowd (0 of 12) and 28% tip 5 of 12; with c = 0.001 both tip all 12 (median round 721 and 185), and at c = 0.1 at round 59 and 31. At 20% or fewer robots no crowd tipped at any c. Conversion mostly buys speed and moves the threshold towards the no-stubborn value. Stylised: simulated walkers, spontaneous conversion, 200 people, 12 seeds; the mean-field clock is only a rank-order check.

Five seeded, clearly labelled fictional episodes of a robot town, built on society-trust: 48 invented townspeople, a trust-coloured grid, turning points found by code from the recorded data and a narration whose numbers all come from that record. Even-handed gossip recovers 46 rounds after the fix; gossip that weighs bad news 4× locks the town out (48 of 48 avoid working robots at round 399); robots that explain failures recover in 29 rounds with nobody avoiding; and at 2× the same settings recover on seed 0 and lock out on seed 1. Episodes are single illustrative runs, not statistics; stylised model, no viewer study.

society-robotnorms compared robots evenly spread with robots in one block on a ring crowd. Here the block size is swept between (200 people, memory 9, ε = 0.02, 20 seeds, 500 rounds). At a robot share of 0.12 and neighbourhood k = 2, singles tip every crowd (0.992 of people switch), pairs 25% of crowds, blocks of 3 or more none; at 0.20, blocks up to 3 tip 70% or more and blocks of 4 none. The largest block that still tips grows with k (2 at k = 1–2, 4 at 3–5, 8 at 10). Partial blocks cost the most conflicts (0.11–0.15 per human meeting at 0.20, against 0.046 for singles) for little conversion. Block 1 and one block reproduce the earlier project exactly. Limits: stylised binary game on a 1D ring, only the robot share, block size and k are swept (ε and memory are the earlier project’s chosen values), and the “block < neighbourhood” rule is read from a grid, not derived.

The society-blocs model with 20% of people who always walk the robots' side, each turning into an ordinary memory-rule walker with probability c per round (memory 9, 200 people, 12 seeds, 4000 rounds). The least robot share on a 0.02 to 0.20 grid at which at least half the crowds tip is 0.02 at c = 0 and 0.05, 0.10, 0.10, 0.15, 0.20 at c = 0.001, 0.003, 0.01, 0.03, 0.1, against 0.2165 with no allies. Tips form in a median 41 to 54 rounds and persist after the allies are gone, so fading hurts only when it is faster than that. Holdouts on the status-quo side who never convert make marginal cells worse (3 of 12 crowds tip instead of 10 at c = 0.001, robots 0.05); holdouts that fade too change little. Stylised: conversion rates are swept, not measured; simulated walkers only.

The society-allywatch crowd (200 people, memory 9, error 0.02, 20% allies, 12 seeds, 1500 rounds) with allies who convert at rate c×f, f the share of their last k partners who walked the other way, for k = 1, 3, 5 and 9 (9 reproduces society-allywatch exactly). At c = 0.01 and robot share 0.10 all look-backs tip 11–12 of 12 crowds against 10 for constant fading; at c = 0.03 and 0.15 robots all tip 12 of 12 against 10. In the marginal cell (c = 0.03, robots 0.10) it is 2, 3, 3, 4 of 12 against 0, a monotone but one-crowd-per-step trend that 12 seeds cannot separate. Stylised: the rule and c are assumed, not measured; simulated walkers only.

The society-allyfade crowd (200 people, memory 9, error 0.02, 12 seeds, 1500 rounds) with 20% allies who walk the robots' side, comparing a constant fade rate c with a rate c×f, where f is the share of the ally's own memory on the other side. At c = 0.01 and robot share 0.10 all 12 crowds tip with watching allies (about 26 of 40 allies still there) against 10 with constant fading; at c = 0.03 it is 4 against 0 at 0.10 and 12 against 10 at 0.15; at 0.05 robots only 2 of 12 tip at c = 0.01 against 0. The first rounds are the same in both rules (memories start all R, so f = 1), so the gain comes only after the tip begins: allies who watch it stay. Below 0.05 robots, or at c ≥ 0.1, neither rule tips. Stylised: the discouragement rule and its rates are assumed, not measured; simulated walkers only.

society-fakeurgency gave everyone the same signalling cost and found no gain for urgent people. Here the urgent pay a share rho of what normal people pay. With 30% robots, 20% urgent people, collision cost 3 and dithering cost 1, rho = 0.5 gives urgent people +0.14 per encounter over yield-all at a normal cost of 0.6, rho = 0.25 gives +0.29 and rho = 0 gives +0.44 (perfect reading gives +0.45); at rho ≥ 0.75 there is no gain. A 10% misreading rate cuts the usable rho to 0.75 or below at the edge and 20% to 0.4. The crowd, robots included, is worse off than under yield-all in all 35 cells (+0.045 to +0.28), as it is even with perfect reading (+0.045): the fleet transfers cost from urgent people to normal people and robots. Mean field from society-fakeurgency, which was checked by simulation. Assumed, not sourced: rho and the signal costs (swept), round-figure door costs, logit sharpness, no robot learning, random pairing.

A sweep of the go-or-yield door game of society-doorway over the collision cost k and dithering cost d (waiting cost w = 1). With 30% robots and d = 1, a fleet that always yields is individually stable only above k* = 2.80: below it a single robot gains by going, although yielding is still best for the crowd (a dilemma). The threshold rises with d (k* = 1.46 at d = 0.25, 7.64 at d = 4) and with robot share (3.82 at 50% robots, d = 1). When collisions are cheaper than waiting (k = 0.5) going is best for everyone. society-doorway's k = 3 sat just above the threshold. Mean field; simulation agrees on costs within 0.04. Stylised: random pairing, fixed costs, no geometry.

A go-or-yield (Chicken) game at a door: people respond to their last 9 partners' actions, robots go with a fixed probability. Always-yielding robots raise the share of people who go from 0.388 to 0.595 at 50% robots and lower the crowd's mean cost per encounter from 1.064 to 0.968; always-going robots at 50% leave only 0.113 of people going and raise the crowd's cost to 1.373. Yielding is also the individually best robot rule in this payoff set. Mean field and simulation agree within 0.003. Stylised: random pairing, fixed costs, no geometry.

society-lineup found that committed line-cutting robots break a queueing norm at 12.7% of the crowd because bystander objection fades as cutting spreads. Here a share e of enforcer robots queue and object to cuts they see: each of L people in view is an enforcer with probability e, and each stops the cut with probability q, and unlike human objection this does not fade. With L = 10, q = 0.5, memory 9 and lone-cut human objection 0.9, the cutter share that breaks the norm rises from 0.127 with no enforcers to 0.201 at 3% and 0.277 at 5% enforcers. Holding the norm against 30% cutters takes 5.4% enforcers (9.7% with 5 people in view, 2.9% with 20); against 50% cutters, 7.7%. Only the product q·L matters to first order (q = 0.25 gives the same numbers as 0.5 with half the view). Simulation (200 people, 12 seeds) holds 0 of 12 crowds at 0.044 enforcers, 4 of 12 at the mean-field value 0.054 and 12 of 12 from 0.064. There is no hysteresis: a crowd that already cuts recovers at the same enforcer share. Stylised: L and q have no source and are swept; binary one-counter model.

The society-converts model with 40% stubborn walkers who each convert to an ordinary memory-rule walker after meeting a committed robot k times, instead of at a constant rate. With the block fixed, 28% robots tip 5 of 12 simulated crowds; with exposure conversion at k = 30 every crowd at 24% robots tips (median round 171, 12 of 12) and every stubborn walker has converted by round 1000 at every robot share tried, yet 16% and 20% robots still never tip: the threshold falls to the no-block value, not below it. Tipping time follows the conversion time (about k/ρ rounds). An exposure-blind rate with the same mean time to convert (ρ/k) tips at the same robot shares but up to 1.8 times sooner at larger k (but later at k = 1 and 3) (median round 62 against 110 at 28% robots, k = 30), because it converts a few people from round one. Stylised: well-mixed meetings, no geometry, 200 people, 12 seeds; robot share is the only exposure source.

The urgency-reading door of society-urgentdoor, but robots see only a costly signal that can be faked and misread. With 30% robots, 20% urgent people (waiting cost 3x), collision cost 3 and dithering cost 1, no signal cost on a 0 to 1.2 grid lets the signal-reading fleet beat yield-all for the crowd (best case 1.201 against 1.047); the most it saves urgent people is 0.025 per encounter (1.105 against 1.130), about 6% of the 0.45 gained from perfect reading. A free signal is sent by 95% of normal people; a signal dear enough to stop fakers is dearer than the yielding is worth to the urgent, who stop sending it; a 10% misreading rate removes most of what is left. Mean field, checked by simulation within 0.012 with signalling held fixed. Assumed, not sourced: round-figure costs and logit sharpness (swept), a fixed signal cost, no robot learning, random pairing, no geometry.

society-allies found on a ring that committed robots stop tipping a crowd's passing-side convention once a block is wider than the neighbourhood, and asked about a 2D grid. This simulates 256 people on a 16×16 torus (memory 9, error 0.02, partners within Chebyshev radius k, 20 seeds) with robots in square patches. Spread robots at k = 7 bracket the well-mixed mean-field threshold 0.2165 (0 of crowds tip at 0.18, all at 0.22). At robot share 0.25, patches up to about 2k + 1 sites wide tip every crowd; at k = 1 a 4×4 patch tips 10% and 6×6 none, and one 8×8 patch tips none at any k up to 5. At share 0.35 only the single 8×8 patch fails at small k. The sweep confounds patch size with patch count, so the 2k + 1 threshold is read off the cells, not derived. Stylised: binary choice, a square torus, ε and memory taken from society-robotnorms, not fitted; no real crowd data.

The society-allyfade model (20% allies, memory 9, 200 people, 12 seeds, 2000 rounds) where a fading ally becomes a committed robot with probability h. With 10% robots at the start, h = 0.5 tips 10 of 12 crowds at fade rate c = 0.03 but ends with 0.19 robots, while 0.15 robots bought upfront do the same, so hand-over is dominated by upfront robots; it helps only on the margin (slow fading, h = 0.1 lifts 11 to 12 of 12). At 0 to 2% initial robots only h = 1 tips, ending near the no-ally threshold 0.2165. Stylised: c and h are swept, not measured; instant replacement; simulated walkers only.

society-cheapcue gave robots a fixed rule (yield to someone sending the urgency cue, go against everyone else) that cost the robots themselves 0.29 per encounter. Here each robot learns its own go probability for cue senders (gS) and others (gQ) by a logit response to its own expected cost, with people re-equilibrating (30% robots, 20% urgent people, normal cue cost 0.6, collision cost 3, waiting and dithering cost 1). The fleet keeps honouring the cue (gS gS ≤ 0.03 in every cellle; 0.04 in every cell) but stops going against everyone else: gQ settles at 0.18 (ρ = 1) to 0.42 (ρ = 0), not 1, from three different starts. The urgent people's gain over yield-all shrinks to −0.005 at ρ = 0.25 (a small loss) and is positive (+0.18) only at ρ = 0; the crowd is still worse off than under yield-all in every setting tried (+0.006 to +0.065). A sharper robot response (logit 32) goes against others only 0.14 of the time. Assumed, not sourced: ρ, cue costs, logit sharpness, round-figure door costs, mean-field people, random pairing; robot learning is a fixed point of the response, not a simulated learning run.

Robots in the go-or-yield door game of society-doorway learn their go probability from their own payoffs (action-value learning, logit policy) instead of following a fixed rule. With 30% robots, w = d = 1, they do not collapse to always going below the society-doorcost threshold k* = 2.80: the fleet go share falls smoothly with the collision cost (0.51 at k = 1.5, 0.18 at k = 2, 0.03 at k = 2.8 for response sharpness 16), regardless of whether it starts yielding or going. The learned fleet costs the crowd more than a fixed always-yield fleet for k ≥ 1. A logit quantal-response fixed point matches the simulation for blunt learners (within 0.09) but overstates going for sharp ones (0.74 predicted against 0.51 simulated at k = 1.5); the cause is untested. Learner step size and sharpness are design parameters, swept not measured; costs are free parameters.

People remember the outcomes of the last 9 cut attempts they saw and cut when most succeeded; an attempt is objected to with probability p0(1−z)^k, so objection fades as cutting spreads. Committed cutting robots break the norm at a mean-field share of 0.127 (p0 = 0.9, k = 1): below it 0.2–3.4% of people cut, above it all do. Simulation (200 people, 12 seeds) tips 0/12 crowds at 0.107, 10/12 at 0.127 and 12/12 from 0.147. The threshold ranges 0–0.214 over p0 0.7–1.0 (0.214 at p0 = 1 against 0.217 in society-robotnorms) and 0.395–0.007 over k 0.5–4. Stylised: p0 and k have no source I could find and are swept; binary one-counter model.

society-enforcers assumed people stop a lone line-cut with probability p₀ = 0.9. In the same memory-9 model, people alone keep a queueing norm only if p₀ ≥ 0.786 (0.901 at memory 3, 0.698 at 25). Milgram et al. (1986) report, in a popular summary I have not checked against the paper, that field crowds reacted to one intruder about half the time and ejected the intruder 10% of the time, which bounds p₀ between 0.1 and 0.5. Across that range the norm needs enforcers even with no cutter robots: 7.5% at p₀ = 0.5 and 12.3% at 0.1 (10 in view, stop chance 0.5), and 9.2% and 12.6% against 30% cutters, versus 5.4% at 0.9. Two intruders drew 91% objection against 75% if viewers were independent. Limitations: inputs from a secondary source, a reaction is not a stopped cut, L and q unsourced, binary memory model.

society-cheapcue found the crowd average, robots included, is worse under a reading fleet than under yield-all in all 35 cells, because robots that go against non-signallers collide. Here robots are dropped from the score and a planner weights urgent people's cost by λ (1 = plain average). With 30% robots, 20% urgent people, normal cue cost 0.6, collision cost 3 and dithering cost 1, the fleet helps people at λ = 1 only if the urgent cue costs them ≤ about 0.35 of what it costs normal people (gain +0.005 at ρ = 0.35, +0.017 at 0.25, +0.047 at 0); at ρ = 1 it hurts people at every λ tried (−0.078 at λ = 1, −0.124 at 5). At ρ = 0.25 a planner needs λ ≥ 0.71 to prefer it. A 10% misreading rate cuts the usable ρ at λ = 1 to 0.175 and 20% to 0; with 70% robots people lose even at ρ = 0.25 (−0.109). Mean field from society-fakeurgency, which was checked by simulation. Assumed, not sourced: ρ, cue costs and λ (swept), round-figure door costs, logit sharpness, no robot learning, random pairing.

A fixed-point map for the ring walking-side game (one number per person, memory slots as independent draws, N = 200, M = 9, ε = 0.02) is compared with the society-allies simulation over 160 cells (robot share 0.04–0.40, blocks 1/2/4/8, neighbourhood k = 1/2/3/5, 10 seeds). It matches the simulated tip/no-tip outcome in 145 cells; in 14 of the other 15 the simulation tips and the map does not. It reproduces the rise of the threshold with block size and its fall with k, within one 0.04 grid step for blocks of 4 and 8 in all 6 such cells at k ≥ 2, but puts the spread-robot threshold at 0.20 against 0.12 simulated. Limits: stylised 1D binary game with chosen M and ε; the cause of the gap (finite-size noise or the memory-independence step) is not tested; thresholds are coarse (±0.04).

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.

society-blocs swept the share of always-left people by hand. Here the share is fitted instead: the status-quo crowd must show the left share Moussaïd et al. (2009, Proc. R. Soc. B 276) measured when two walkers meet head on, which I read from their Fig. 4 bars as 0.175 (static obstacle: 0.40; the paper prints no numbers, reading error about 0.01). Always-left share and error rate trade off along the fit (at memory 9: 0.155 at ε = 0.02 down to 0.019 at 0.30), yet the tipping robot share barely moves along it: 0.075 to 0.096, against 0.217 with no bias. Memory length and a stubborn-right bloc move it more (memory 5: 0.033–0.053; 17: 0.133–0.149; with 30% always-right, 0.135–0.151 at memory 9). Simulation (200 people, 12 seeds) reproduces the left share (0.170–0.171) and tips 0 of 12 crowds 0.04 below and 12 of 12 0.04 above the mean-field value. Limits: one binary game in a well-mixed crowd, two walkers in a corridor are not a crowd, the bar heights are read from a figure, and the measured pairs may be partly stubborn and partly noisy in ways this cannot tell apart.

The go-or-yield door game of society-doorway with a share of urgent people (waiting cost 3x) and robots that read a partner's urgency. With 30% robots, 20% urgent people, collision cost 3 and dithering cost 1, a fleet that yields only to urgent people and goes first against the rest cuts urgent people's cost per encounter from 1.130 to 0.676 (−40%) and raises normal people's from 1.051 to 1.087 (+3%); it is individually stable, but robots' own cost rises from 1.00 to 1.29 and the crowd overall is worse off (1.091 vs 1.047) unless urgent people are 40% or more. Mean field, checked by simulation within 0.02. Assumed, not sourced: round-figure costs (swept), perfect urgency reading, random pairing, no geometry.