Most real decisions involve tradeoffs among multiple attributes — a job candidate has salary, location, and culture; a treatment has efficacy, side effects, and cost. Multi-Attribute Utility Theory (MAUT), developed by Keeney and Raiffa (1976), provides the axiomatic conditions under which a multi-attribute utility function can be decomposed into simpler functions of individual attributes.
Decomposition Forms
Multiplicative: Π(1 + k·wᵢ·uᵢ) = 1 + k
Multilinear: U = Σwᵢuᵢ + Σwᵢⱼuᵢuⱼ + ...
The additive form applies when the attributes are mutually preferentially independent: preferences over levels of one attribute do not depend on the levels of other attributes. If this condition is weakened to utility independence, the multiplicative form is appropriate. The multilinear form accommodates limited interactions between attributes.
Practical Application
In practice, MAUT involves (1) identifying relevant attributes, (2) assessing single-attribute utility functions uᵢ, (3) estimating weights wᵢ through tradeoff questioning or swing weighting, and (4) checking the structural assumptions. MAUT has been applied to medical decision making, environmental policy, engineering design, and personnel selection. Its axiomatic foundation ensures that the resulting recommendations are logically coherent given the assessed values.