Reasoning about optimal stable matchings under partial information
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Bibliographic record
Abstract
We study two-sided matching markets in which participants are initially endowed with partial preference orderings, lacking precise information about their true, strictly ordered list of preferences. We wish to reason about matchings that are stable with respect to agents' true preferences, and which are furthermore optimal for one given side of the market. We present three main results. First, one can decide in polynomial time whether there exists a matching that is stable and optimal under all strict preference orders that refine the given partial orders, and can construct this matching in polynomial time if it does exist. We show, however, that deciding whether a given pair of agents are matched in all or no such optimal stable matchings is co-NP-complete, even under quite severe restrictions on preferences. Finally, we describe a polynomial-time algorithm that decides, given a matching that is stable under the partial preference orderings, whether that matching is stable and optimal for one side of the market under some refinement of the partial orders.
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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 | 0.001 | 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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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