A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions,
RAND CORP SANTA MONICA CALIF
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This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions the additive, Keeneys quasi-additive, Fishburns diagonal, and others. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations which are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes apex, diagonal, quasi-pyramid, and semicube. The methodology is illustrated with geometric structures that correspond to the fractional hypercubes.
- Operations Research