Correcting illegitimate rank reversals: proper adjustment of criteria weights prevent alleged AHP intransitivity
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Bibliographic record
Abstract
Abstract This note comments on a paper by Triantaphyllou ( J. Multi‐Crit. Decis. Anal. 2001; 10 : 11–25) that attempts to demonstrate new types of rank reversal that can occur with the analytic hierarchy process (AHP). He contends that the reversals are attributable to the various types of normalization that are used with the addition step in AHP synthesis. His paper goes on to suggest that the multiplicative AHP should be used instead. This note shows that the cause of the problem is another one: AHP's independence axiom, which prohibits adjusting the criteria weights when the set of alternatives or the type of normalization change. If the criteria weights are adjusted properly, none of the rank reversals will occur. Copyright © 2009 John Wiley & Sons, Ltd.
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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 | 0.017 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.000 |
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