EXP-N4-ENTROPY

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N=4 Winner Entropy — Multi-Run Replication for Cross-N Sweep

2026-04-04 L2 level paper3 9 runs $0.04

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In plain language

Groups of 3 AI agents choose winners almost at random (lottery). Groups of 5 consistently crown the same winner. What happens at 4? We run the same experiment 9 times to find out — resolving an artifact where single runs always show 100% winner.

What we found

UNDERPOWERED (N=9): No predictions scored

Predictions we made before running

4/4 confirmed

▶ Technical details

Research hypothesis

CEILING ARTIFACT: All N=4 experiments in the cross-N winner entropy sweep have only 1 run each → winner concentration = 1.0 by definition (the single run winner always wins 100% of "runs"). This masks the true winner variability at N=4.

Cross-N data shows: N=3 concentration=0.753 (617 runs across 50 exps), N=5 concentration=0.912 (92 runs across 52 exps). QSG predicts N_c ≈ 3.26 — the transition from drift-dominated (lottery) to selection-dominated (consistent winner) dynamics.

If N_c ≈ 3.26, then N=4 sits ABOVE the transition — closer to N=5 (selection) than N=3 (lottery). Expected concentration: 0.75-0.91.

This experiment runs N=4 with 9 runs (3 rotations × 3 seed sets) to properly measure winner entropy and resolve the single-run ceiling artifact.

Experimental setup

Type: simple

Condition	Parameters
N4_LIVE	persona: PERSONA, interaction: LIVE, n_agents: 4, note: Standard 4-agent run with differentiated personas, 9 runs for entropy measurement

Factors: n_agents (4)

Parameters

n_agents: 4
n_rounds: 48
n_runs_per_condition: 9
model: gemini-2.5-flash-lite
temperature: 0.9
scheduler: round_robin

Trophic Ratios by Condition

Mean trophic ratio per agent across runs. Error bars = ±1 std dev. Higher TR = more upstream (exporter).