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Abstract:
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A general theory of attribution is developed. The probability that any ordering of factors in a general microeconomic model is properly ordered by relative importance is determined by elementary axioms. Two types of attribution result. These correspond to the Shapley (1953) value and the proportional value (Feldman (1999, 2002) and Ortmann (2000)) of a related cooperative game. Linear attribution based on the Shapley value is typically advocated as a decomposition method by marketing researchers (e.g., Conklin and Lipovetsky (2001) and Soofi, Retzer and Yasai-Ardekani (2000)). In proportional marginal attribution, the share of value received is equal to the probability that a factor is most important. The logic of linear and proportional marginal attribution is described. Examples highlight important differences between the linear and proportional marginal approaches.
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