Seed a room where one member in twenty-five refuses to bend. One veto decides a cell of four; four cells decide a block; blocks decide districts — and the whole map flips. The arithmetic below is exact; the veto it runs on is the admitted cartoon.
The claim is Taleb’s: Skin in the Game, Book 3, chapter 2 — an intransigent minority of a few percent can flip a whole population, because the choice is asymmetric: the flexible eat anything, the intransigent do not. His running example is drinks — someone keeping kosher or halal will not drink the non-compliant version, while the flexible drinker takes either; once compliance is cheap it is simpler to make every drink compliant, so nearly all mass-market drinks quietly end up kosher and the majority never notices. The flip climbs by renormalization — person, family, neighborhood grocer, wholesaler, society — provided the minority is spatially dispersed and the cost of compliance stays small. The essay version is online as The Most Intolerant Wins.
The model on this page is the standard cartoon of that chapter, and it confesses. The engine: a unit of four serves the strict option the moment one member is intransigent — a universal veto — so the strict share climbs by the exact map pk+1 = 1 − (1 − pk)4. That map has only two fixed points, 0 and 1, and f′(0) = 4 > 1: zero is unstable, so the toy has no threshold at all — any q > 0 cascades to 1 (q = 0.1% gets there in 7 levels, q = 10−6 in 12). The observed real-world threshold — Taleb’s three-to-four percent — must therefore come from what the veto model omits: cost, distance, exit, the option not to share the menu. The one-shot version of the same arithmetic is the neighborhood formula 1 − (1 − q)k, the chance that a circle of k people contains at least one intransigent (at q = 4%, k = 9 it reads 0.30747). And a small-sample honesty note: the lattice’s top rows are tiny — 24 districts, then 6 regions — so the mint dots wobble around the purple line; the map is the model’s truth, the lattice one seeded draw of it.
Salt: the cascade is honest arithmetic exactly where vetoes are real — a dietary law on a shared menu, a safety rule on a shared production line, one non-drinker deciding what the party serves. Where nobody actually holds a veto — where the majority can shrug, pay, or leave — the same curve is a cartoon of one, and reading it as a forecast of any particular flip would be exactly the error this wing exists to fence.