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EXP-QUAD

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Quartet Scaling — Does Hierarchy Deepen at N=4?

2026-03-08 L3 level paper3 1 runs
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In plain language

Two agents can't form hierarchy. Three can. What about four? We add a fourth agent — a storyteller — to see if the pecking order deepens or if three levels is the ceiling for this kind of interaction.

Predictions we made before running

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0/4 confirmed · 3 refuted · 1 borderline

▶ Technical details

Research hypothesis

EXP-DYAD: N=2 produces NO hierarchy (TR diff 0.060, direction inconsistent). EXP-ASYM: N=3 produces STABLE hierarchy (TR diff 0.444, Gamma upstream 9/9).

Question: does adding a 4th agent DEEPEN the hierarchy (wider TR spread, more trophic levels) or SATURATE it (same 3-level structure, 4th agent collapses into existing level)?

Gershenson predicts: more agents = more interaction graph edges = more possible asymmetric flow paths = deeper hierarchy (up to substrate limit).

Alternative: 3-level hierarchy is the maximum for this prompt/persona space — the grounding/associative/analytical axis has only 3 natural endpoints. A 4th persona (narrative/synthesis) maps onto an existing cognitive style axis position.

Delta persona: narrative synthesis — weaves threads, connects across time. Prediction: if hierarchy scales, Delta occupies a UNIQUE trophic level (midstream integrator). If saturates, Delta collapses onto Alpha's level.

Experimental setup

Type: simple

Condition Parameters
QUAD_LIVE persona: PERSONA, interaction: LIVE, n_agents: 4

Factors: n_agents (4)

Parameters

n_agents
4
n_rounds
48
n_runs_per_condition
1
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).