A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion
Bibliographic record
Abstract
Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing the relative efficiency of decision making units (DMUs). The cross-efficiency evaluation is an extension of DEA that provides a ranking method and eliminates unrealistic DEA weighting schemes on weight restrictions, without requiring a prior information. The cross-efficiency evaluation may have some shortages, e.g. the cross-efficiency scores may not be unique due to the presence of several optima. To rectify this issue, several secondary goals have been proposed in the literature. Some scholars have proposed several cross-efficiency evaluations based on maximising (minimising) the total deviation from their ideal point as an aggressive (benevolent) perspective. In some cases, minimising (maximising) the number of DMUs that achieve their target efficiencies, is more important than maximising (minimising) the total deviation from the ideal point. We propose some alternative models for the cross-efficiency evaluation based on the cardinality of the set of “satisfied DMUs”, i.e. the DMUs that achieve their maximum efficiencies. For aggressive (benevolent) cross-efficiency evaluation, among all the optimal weights for a specific unit, we choose the weights which can maximise its efficiency, and at the same time minimise (maximise) the number of satisfied units. We demonstrate how the proposed method can be implemented and illustrate the method using two examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.022 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.006 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".