Probabilistic Analysis of the Efficacy of Periodic Testing of Employees
Bibliographic record
Abstract
Some major companies have the policy of annually giving numerical scores to their employees according to their performance, firing those whose performance scores are below a given percentile of the scores of all employees, and then recruiting new employees to replace those who were fired. We introduce a probabilistic model to describe how this practice affects the quality of employee performance as measured over time by the annual scores. Let n be the number of years that the policy has been in effect, and let F n ( x ) be the distribution function of the evaluation scores in year n . We show, under certain technical assumptions, that the sequence ( F n ( x )) satisfies a particular nonlinear difference equation, and furnish estimates of the solution of the equation and expressions for the quantiles of F n . The mathematical tools that are used include convex functions, difference equations, and extreme value theory for independent and identically distributed random variables.
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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 | 0.003 | 0.022 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".