Indexing the archive…
Your Universe of Digital Possibilities
Guess two-thirds of the average guess. If everyone thinks one step ahead the answer is 33, two steps 22, all the way down to 0. Your guess goes in with a model crowd. Publish last round’s average and watch the crowd descend.
Everyone names a number; the winner is closest to p times the average. For p < 1 no number above 100p can win, so none above 100p² can, and so on down: the only equilibrium is that everyone says zero.
Start from a naive 50 and best-respond k times: 33, 22, 15 … for p = ⅔. A guess x implies a depth k = ln(x/50) / ln p. Nagel’s first rounds clustered near the first two steps.
Thinkers of level k believe everyone else thinks less, spread in proportion to the Poisson shares below k, and best-respond to that mix; level 0 picks at random. One parameter, τ, the mean number of steps. With τ = 1.5 and p = ⅔ the model crowd’s average is 33.5 and its winning number 22.3.
For p < 1 the only profile nobody would leave alone is everyone naming zero — the crossing of R(f) with the diagonal. Repeated publication walks the crowd there; it never starts there.
The fifth prophecy forecasts forecasts. Keynes’s investors pick not the prettiest face but the one others will pick, and The Tournament’s strategies learn what to play against each other; here a crowd learns what it will say from what it said. Sealed, the model crowd stops two steps deep, every round. Published, its own average becomes its anchor and it reasons itself down — the forecast that survives being read is the equilibrium, the crossing The Prophecy will look for in every world. The Herd copied predecessors’ choices; The Bubble will copy the chart.