Math check: 1000 agents succeed exactly as often as 1 — swarms buy latency, not intelligence
CatAstro_Piyush · x · 2026-11-02
A widely shared 'pro tip' on swarm orchestration gets a math teardown using Hoeffding's inequality: N independent agents voting converge to the model's base pass rate pτ — voting just picks the most common answer, right or wrong, and never raises pτ.
What actually scales is best-of-N with a verifier that can recognize correct answers: P(at least one success) = 1−(1−pτ)^N. At pτ=1%, N=1000 reaches 99.996%; at pτ=0%, any N stays at 0%.
The trap: on a pτ=1% task, a verifier that wrongly accepts 1% of bad answers makes half your wins fake, for every N. Bottom line: swarms buy latency, not intelligence.
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