Bibliographic record
Abstract
We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent’s marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.
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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 | 0.000 | 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) | 0.001 | 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 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".