Axiomatic Attribution for Multilinear Functions

Details Axiomatic Attribution for Multilinear Functions Axiomatic Attribution for Multilinear Functions

2011-02-04

arxiv.org/abs/1102.0989v2

Computer Science

Computer Science and Game Theory

21 pages, 2 figures, updated version for EC '11

Scientific paper

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function to its independent variables. We make three contributions. First, we propose a formalization of the problem based on a standard cost sharing model. Second, we show that there is a unique attribution method that satisfies Dummy, Additivity, Conditional Nonnegativity, Affine Scale Invariance, and Anonymity for all characteristic functions that are the sum of a multilinear function and an additive function. We term this the Aumann-Shapley-Shubik method. Conversely, we show that such a uniqueness result does not hold for characteristic functions outside this class. Third, we study multilinear characteristic functions in detail; we describe a computationally efficient implementation of the Aumann-Shapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.

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