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EXP-DYAD

informative

Dyadic Emergence Threshold — Minimum N for Trophic Hierarchy

2026-03-08 L3 level paper3 4 runs
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premortem
mock
real
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done

In plain language

Two agents are not enough for hierarchy. Three is the minimum. Like in chemistry: you need a third element for a directed reaction to emerge. A pair just exchanges words without structure.

What we found

UNDERPOWERED (N=4): No predictions scored

Predictions we made before running

0/4 confirmed

Technical details

Research hypothesis

Role differentiation (trophic hierarchy) requires N≥3 agents. At N=2 (dyad), the system lacks sufficient interaction topology for emergent role structure: with only one directed relationship, there's no "downstream" vs "upstream" distinction (only A→B or B→A).

Gershenson's E (emergence) predicts: the global pattern cannot emerge from pairwise interaction alone — three-way dynamics (A influences B who influences C who influences A) create the closed behavioral loop necessary for stable roles.

EXP-ASYM showed N=3 PERSONA_LIVE produces stable hierarchy (TR Friedman p=0.008). This experiment tests N=2 with the same personas that had the STRONGEST differentiation (Gamma upstream TR=0.724, Beta downstream TR=0.280). If even the most differentiated pair fails to produce hierarchy, N=3 is a genuine emergence threshold.

Alternative hypothesis: N=2 DOES produce hierarchy because persona asymmetry alone is sufficient — the grounder→upstream pattern operates in any dyad via vocabulary specificity mechanism.

Experimental setup

Type: simple

Condition Parameters
DYAD_LIVE persona: PERSONA, interaction: LIVE, n_agents: 2

Factors: n_agents (2)

Parameters

n_agents
2
n_rounds
12
n_runs_per_condition
2
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).