The Equal Share Proportional Solution for the River Sharing Problem
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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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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 | 0.003 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it