Concept

Efficiency

The property of an allocation that no alternative makes someone better off without making someone else worse off. It is also called Pareto optimality, and it is the condition that fairness rules are most often forced to trade against.

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

Drop one condition, and something else satisfies the rest. A column for each of the four conditions, holding a sharing rule that breaks that one and keeps the other three, with the split each rule gives on a stated four-player game.

None of the four conditions is spare

Four conditions pick out one sharing rule. The half that is usually shown is that they are enough; the other half is that each is needed — drop any one and a different rule satisfies the rest, so the list cannot be shortened.

applied · Shapley value

Maximising the product of two people's values. The frontier of value pairs from dividing 4 goods between two people, with the points maximising the product, the sum and the smaller value. The product's maximum is (65.0, 54.2) and is envy-free.

The product that makes a division fair

Divide goods to make the total happiness as large as possible and the result can be monstrously unfair; make the least happy person as happy as possible and it can waste. Multiply the people's values together and maximise the product instead, and something unexpected happens — nobody envies anybody when goods can be split, and nobody envies by more than one item when they cannot.

applied · Fair division

Named alongside it

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

Additivity Allocation Axiomatic characterisation Convexity Cooperative game Duality Envy-freeness Fair division Independence of axioms Indivisible goods Marginal contribution Null-player

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