When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?
Why this work is in the frame
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Bibliographic record
Abstract
The symmetric equilibrium resulting from the celebrated Tournament model of Lazear and Rosen has a range of compensation between winner and loser which is inversely proportional to E[f(X)], the expectation of the additive noise's density. There seems to be a belief that this functional is always increasing in the noise's variability, which would agree with economic intuition — when output is noisier it should be less worthwhile to work hard. We show that such is not the case for some distributions, and characterize classes where such is or is not the case. When the number of players n grows, winning is more difficult so we would expect the required range of compensation to be larger. That would require that E[f(Y)], where Y = max (X 1 ,…,X n-1 ), will decrease in n. We examine the generality of this property. Finally we explore the same issues within a multiplicative model.
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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 | 0.005 | 0.001 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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