On comparisons of information structures with infinite states
Why this work is in the frame
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Bibliographic record
Abstract
Blackwell's theorem on the comparison of information structures is by now sufficiently well-understood for a finite state space, but important gaps remain in the infinite case. While the equivalence of (i) sufficiency and (ii) more-informativeness is known, we present a comprehensive theory that establishes equivalences between these two orders (in both their original and almost all versions) and three additional prior-dependent criteria on general (Polish) state spaces. We consider (iii) Bayesian preference, (iv) convex dominance, and (v) mean-preserving-spread (dilation) for all priors as well as for a given full-support prior. We provide counterexamples to underscore the necessity of the assumptions underlying some of our findings, and offer a generalization of the Hirschleifer-Schlee theorem as an application.
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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 | 0.001 | 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