Axiomatic Attribution for Multilinear Functions

We study the attribution problem, that is, the problem of attributing a change in the value of a characteristic function f 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 AumannShapley-Shubik method and discuss practical applications to pay-per-click advertising and portfolio analysis.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Yi Sun, Mukund Sundararajan
• Keywords: Characteristic Functions, CORR 2011, Education, Multilinear Characteristic Functions, Unique Attribution Method