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 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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| 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) | 0.009 | 0.014 |
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; both teacher heads agree on what is shown here.
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".