The Equal Share Proportional Solution for the River Sharing Problem
Bibliographic record
Abstract
This paper considers the river sharing problem first studied in Ambec, S. and Sprumont, Y. [2002] Sharing a River, J. Econ. Theory 107, 453–462. We use the Equal Share Proportional Solution (ESPS) for the permit sharing problem introduced in Suh, S. and Wang, Y. [2023] The equal share proportional solution in a permit sharing problem, Soc. Choice Welf. 60, 477–501 to define a solution, also called the ESPS, for the river sharing problem. We first show that a river sharing problem can be divided into a list of subproblems, each of which can be considered as a permit sharing problem (Decomposition Lemma). Then, we apply the ESPS solution to each of the subproblems. The ESPS for the river sharing problem is the aggregation of the ESPS for all the subproblems. We also compare the ESPS with the well-known Downstream Incremental Distribution solution (DID) by Ambec, S. and Sprumont, Y. [2002] Sharing a River, J. Econ. Theory 107, 453–462. We show that for a dummy agent whose optimal consumption coincides with his initial endowment, the agent obtains his stand-alone benefit in the ESPS. In contrast, the DID solution may assign welfare levels to dummy agents that are higher than their stand-alone benefits. On the other hand, the ESPS violates the aspiration upper bounds.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.015 | 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".