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Order out of noise — page 4

Random processes that reliably produce the same shape, and the reason that is less mysterious than it looks.
Evidence as steps on a scale of decibans. A horizontal decibel scale of odds with a starting dot at the prior and one arrow per piece of evidence, ending at a posterior probability of 44.2%. Probability

Evidence measured in decibans

Write a probability as odds and take the logarithm, and every piece of evidence becomes a length. A positive result on a good test is thirteen decibans; a negative one is minus twenty. Lay the lengths end to end from the prior and the posterior is where they stop, in any order. The rule fails in exactly one way — when two pieces of evidence share a cause — and Turing built a code-breaking method on the arithmetic.

 A random ranking on the triangular graph, 8 a side. A bipartite graph in which arrival t is joined to places t through 8. One random ranking of the places is used to match greedily; 5 of 8 arrivals are matched. Discrete

Matching as they arrive

Applicants arrive one at a time, and each must be given a post or turned away on the spot. Any sensible rule matches at least half as many as the best assignment chosen with hindsight, and an adversary arranging the arrivals can hold every fixed rule to exactly half. Shuffle the posts once, at random, and give each arrival its best-ranked free post: the guarantee rises to 1 − 1/e, about 63%, and no rule of any kind can do better.

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