Fair Allocation of Indivisible Items: Consequences of Correlated Preferences
Bibliographic record
Abstract
Fair allocation of indivisible items among multiple individuals is a fundamental problem in collective choice. We consider the problem of allocating two of four indivisible items to each of two players, where the only known preference information is each player's strict ranking of the items. How is the rank correlation of preferences, as measured by Kendall Tau, related to properties that facilitate fair allocation such as the availability of envy-free, Pareto-optimal, maximin, and max BordaSum allocations? We also examine the relationship between the ranked correlation and features of Fallback Bargaining such as the depth of agreement and the probability of a (two-way) tie. We further categorize the players into two types, risk-averse and risk-acceptant, and analyze how player type affects various fair division properties. Our results suggest that increasing similarity of preferences tends to increase the number of Pareto-optimal and maximin allocations but to decrease the number of envy-free allocations. Higher rank correlation also makes Fallback Bargaining less compelling. Understanding how similarity of preference rankings influences the trade-offs among allocation properties gives new insight into the difficulties of fair allocation of indivisible items.
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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 | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".