Multiattribute Utility Functions Satisfying Mutual Preferential Independence
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Bibliographic record
Abstract
The construction of a multiattribute utility function is an important step in decision analysis. One of the most widely used conditions for constructing the utility function is the assumption of mutual preferential independence where trade-offs among any subset of the attributes do not depend on the instantiations of the remaining attributes. Mutual preferential independence asserts that ordinal preferences can be represented by an additive function of the attributes. This paper derives the most general form of a multiattribute utility function that (i) exhibits mutual preferential independence and (ii) is strictly increasing with each argument at the maximum value of the complement attributes. We show that a multiattribute utility function satisfies these two conditions if and only if it is an Archimedean combination of univariate utility assessments. This result enables the construction of multiattribute utility functions that satisfy additive ordinal preferences using univariate utility assessments and a single generating function. We also provide a nonparametric approach for estimating the generating function of the Archimedean form by iteration.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.020 | 0.040 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.009 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it