Best of Both Worlds Fairness under Entitlements
Bibliographic record
Abstract
We consider probabilistic allocation of indivisible items to agents with additive valuations and weighted entitlements. We explore how far ex-ante and ex-post fairness properties can be achieved simultaneously. Our first result is that in contrast to the case of same entitlements, well-established adaptations of ex-ante envy-freeness and ex-post envy-freeness up to one item (EF1) to the case of entitlements are not compatible. We then present a polynomial-time algorithm that achieves weighted ex-ante envy-freeness and ex-post weighted envy-freeness up to 1 transfer. The outcome is ex-ante weighted envy-free for all utilities consistent with the underlying ordinal preferences but it is not Pareto optimal. We then present an alternative polynomial-time algorithm that satisfies Pareto optimality (both ex-ante and ex-post), ex-ante weighted envy-freeness and ex-post weighted proportionality up to one item.
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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 | 0.006 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".