Optimal tradeoff between efficiency and Jain's fairness index in resource allocation
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Bibliographic record
Abstract
In this paper, we study tradeoff policies between efficiency and the Jain's fairness index of the benefits received by M users in general resource allocation scenarios. Analyzing the commonly-used α-fair tradeoff policy, it is shown that, except for the case of M =2 users, this policy does not necessarily achieve the optimal Efficiency-Jain tradeoff. In particular, it is shown that, when the number of users M >;2, the gap between the efficiency achieved by the α-fair and the optimal Efficiency-Jain tradeoff policy can be unbounded, for the same Jain's index. Finding the optimal Efficiency-Jain tradeoff for arbitrary set of admissible benefits is generally difficult. To alleviate this difficulty, we derive sufficient conditions, which, when satisfied by the set of admissible benefits, lead to efficiently computable optimal tradeoff and benefit vectors. Numerical results for a typical communication network scenario are provided to confirm analytical findings.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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