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Concept

Dummy player

A player whose arrival adds nothing to any coalition, whoever is already present. Any fair division gives such a player nothing, and that requirement is one of the four conditions that single out the Shapley value.

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

A share of the votes, and a share of the power. Three weighted assemblies, each with the members' share of the votes beside their share of the power counted two independent ways.

A share of the votes is not a share of the power

Give three members four, four and one vote, with five needed to pass. Every winning coalition needs exactly two of them, so all three have equal power — and one of them holds a ninth of the votes.

applied · Shapley value Credit for one prediction, three ways of leaving an input out. Groups of bars, one group for each way of filling in the inputs that are not known, each bar one input's share of the difference between the prediction and the starting value.

What a missing input is worth

A model prices a house at 180 from its size, its garden and its bedrooms, and the question is how much of the price each input is responsible for. Make the inputs the players and the average over orders answers it — once somebody decides what the model says when an input is not known. Three reasonable decisions give bedrooms nothing, nothing, and sixteen, for a model that never reads them.

applied · Shapley value

Named alongside it

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

Marginal contributionBanzhaf indexConditional expectationCooperative gameEfficiencyFeature attributionInteractionPivotal playerQuotaShapley shubik indexShapley valueSimple game

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