Previous research has found that funding disparities are driven by applications’ final impact scores and that only a portion of the black/white funding gap can be explained by bibliometrics and topic choice. Using National Institutes of Health R01 applications for council years 2014–2016, we examine assigned reviewers’ preliminary overall impact and criterion scores to evaluate whether racial disparities in impact scores can be explained by application and applicant characteristics. We hypothesize that differences in commensuration—the process of combining criterion scores into overall impact scores—disadvantage black applicants. Using multilevel models and matching on key variables including career stage, gender, and area of science, we find little evidence for racial disparities emerging in the process of combining preliminary criterion scores into preliminary overall impact scores. Instead, preliminary criterion scores fully account for racial disparities—yet do not explain all of the variability—in preliminary overall impact scores.

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We propose a new metric for evaluating the informativeness of a set of ratings from a single rater on a given scale. Such evaluations are of interest when raters rate numerous comparable items on the same scale, as occurs in hiring, college admissions, and peer review. Our exposition takes the context of peer review, which involves univariate and multivariate cardinal ratings. We draw on this context to motivate an informationtheoretic measure of the refinement of a set of ratingsentropic refinementas well as two secondary measures. A mathematical analysis of the three measures reveals that only the first, which captures the information content of the ratings, possesses properties appropriate to a refinement metric. Finally, we analyse refinement in real-world grantreview data, finding evidence that overall merit scores are more refined than criterion scores.

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We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Dedicated to Tien-Yien Li, in honor of his birthday.