Social Proof Cascade in Live Commerce

Live Stream Controls

Influencer reach 30%

Social-proof weight 2.0

Scarcity urgency weight 3.0

Initial stock (units) 60

Stream live — waiting for first sale…

Stock

60 / 60 left0 sold

Live Readouts

Conversion rate

0.0%

Cascade depth

0 hops

Purchases via social proof (vs. direct reach)

0 / 0

How it works

Each of the 140 viewer nodes is a Bernoulli trial that fires at most once per stream. Every simulation tick, a viewer i who has not yet bought and while stock remains has purchase probability:

z_i  = w0 + R·w_reach·[reached_i]
          + P·ln(1 + k_i(t))
          + S·max(0, 1 − stock(t)/stock0)

p_i  = 1 / (1 + e^(−z_i))    (logistic sigmoid)

where [reached_i] flags a viewer inside the influencer's direct broadcast fan-out (size set by Reach), k_i(t) counts i's already-purchased graph neighbours (the social-proof term, weighted by Social-proof weight), and the last term is a FOMO/scarcity multiplier that grows from 0 toward 1 as the stock bar empties, scaled by Scarcity urgency weight. w0 is a small negative baseline so a trickle of organic sales happens even with every slider at zero.

Reach — fraction of viewers who see the influencer's on-screen call-to-action directly, independent of their neighbours.
Social-proof weight — how strongly a fresh "Alex just bought this!" notification from a connected viewer pushes their neighbours toward buying (a linear-threshold contagion model).
Scarcity urgency weight — how much a shrinking stock bar accelerates purchases, modelling FOMO as stock → 0.
Cascade depth — the longest chain of "purchase caused a neighbour's purchase" hops traced back to a directly-reached viewer, i.e. how far the social-proof effect propagated through the graph rather than being driven by direct reach alone.
Sales stop the instant stock hits zero — a real flash-sale sellout.

This is the same mechanic that drives live-shopping conversion on TikTok Shop / Instagram Live Shopping: a purchase notification ticker plus a countdown-limited stock bar turn ordinary interest into a self-reinforcing cascade.

Influencer Viewer (not yet bought) Purchased

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