Indexing the archive…
Your Universe of Digital Possibilities
Sixty people choose a restaurant one at a time, each with a private hint and a view of everyone before them. After two agree, the rest stop listening to their own hint. Run the street twice from one seed — the history sealed in one, published in the other — and see why crowds can be confidently wrong.
λ is the public record’s log-odds, s = ±1 the private signal. Once the record leans by more than one signal’s worth, every arrival takes the same door whatever she saw; her action then tells the record nothing and λ stops moving. With binary signals that happens after the first two agreeing choices (a tie is a coin).
The chance the crowd ends up locked on the better door, and on the worse one, for signals right with probability p. At p = 0.6 one crowd in three cascades the wrong way — with a hundred people still to come, each holding a signal that would have helped.
With every signal acted on and counted, a majority of N independent voters, each right with probability p > ½, is right with a probability that tends to one. The sealed street is a Condorcet jury; the published one is not.
Each arrival multiplies the published odds by her signal’s likelihood ratio; the record multiplies them by the likelihood of her action — and an action taken whatever the signal has a likelihood ratio of one. That is the whole of a cascade.
The fourth prophecy is the history itself. The Run published one headline; here every choice is a headline for the next chooser, and two in a row are enough to drown everything that follows. Sealed, the same street is The Ballot’s jury, and the majority comes right; published, it is a herd, right only as often as its first two members were. The Enclave sorts a city by what neighbours see of each other; this sorts a crowd by what it saw of those before it. Next, The Guess asks what happens when what everyone forecasts is what everyone else forecasts.