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arXiv · 2608.23407

Optimal Grading: A Unified Approach

Bin Liu·Jingfeng Lu
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Abstract

We develop a unified approach to optimal grading in an all-pay contest in which a designer assigns a fixed vector of heterogeneous prizes to maximize expected total effort. The approach covers two information regimes and identifies a common principle: iron locally misordered incentive returns and assign prizes assortatively across the resulting grades. Under rank-only grading, assignments depend only on ordinal ranks. Ironing cumulative rank coefficients---via the least concave majorant or the pool-adjacent-violators algorithm---determines which adjacent ranks are pooled and which prizes are randomized within each grade. Under performance-contingent grading, assignments may depend on numerical effort. The optimum irons virtual ability, forms endogenous type grades, and assigns prize blocks assortatively across grades. A failing grade below a minimum passing effort and a collection of effort brackets implement the direct optimum while preserving full prize assignment.

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Bin Liu, Jingfeng Lu. 2026-08-24. Optimal Grading: A Unified Approach. https://arxiv.org/abs/2608.23407

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