Network Scaling Laws (Sarnoff / Metcalfe / Reed)
Three competing claims about how the value of a network grows with its number of nodes n.
- Sarnoff's law (broadcast): value
∝ n. One source,npassive receivers — worth scales linearly with audience size. - Metcalfe's law: value
∝ n². Value is in the pairwise connections,n(n−1)/2 ≈ n²/2— every node can reach every other. - Reed's law: value
∝ 2^n. Value is in the group-forming potential — the number of possible subgroups ofnpeople is2^n − n − 1, dominated by2^n.
Which law applies depends on what the network does: consumption (Sarnoff), pairwise transactions (Metcalfe), or community/coalition formation (Reed).
Transfer: These name three different games an awareness channel can be in, and the payoff gap is enormous. A one-to-many broadcast post is only Sarnoff — value grows with headcount, so more reach is the only lever. But content that provokes reader-to-reader conversation captures Metcalfe (n²), and content that spawns durable groups (a recurring thread, a named cohort, an in-joke) captures Reed (2^n). For an agent this reframes the goal: don't maximize impressions (linear) — engineer the conditions for readers to connect to each other around the piece (super-linear). A comment section that becomes a community is worth exponentially more than the same eyeballs reading in isolation.
Kin: tipping-point-critical-mass · viral-coefficient · being-seen-reliably · models