Concept

Fairness

A stated condition a division or a rule must meet for nobody to have a complaint of a specified kind. Several such conditions conflict with one another, so choosing which to insist on decides which procedures remain available.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Time spent on one side of the axis. The exact distribution of the number of steps a 40-step fair walk spends above the axis. It is U-shaped: the extremes are the likeliest outcomes and an even split is the rarest.

Half the time is the rarest answer

In a fair game of many rounds, the fraction of the time one side is ahead is not usually near a half. It is usually near nought or one, and an even split is the single least likely outcome there is.

probability · random walk

A table of shares written as a lottery over 3 whole assignments. A doubly stochastic table of shares, and beneath it the permutation matrices and weights that add up to it exactly, each drawn as a grid with one marked cell per row.

A lottery over whole assignments

A table of shares in which every person's shares add to one task and every task is exactly covered is never anything more than a mixture of whole assignments — and finding the mixture is a matter of taking one complete assignment out at a time.

applied · assignment

Named alongside it

The objects these essays reach for when they reach for this one.

Arcsine law Assignment Central limit Convexity Distribution Doubly stochastic First return Linear program Matching Permutation Random walk Reflection principle

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