Research

We provide parallel axiomatic foundations for the concave and convex integrals, which represent optimistic and pessimistic rules for aggregating interacting attributes. For the concave integral, we show that the existing characterizations hold once accordance for additive capacities is required for every finite attribute set rather than only when the attribute set is a singleton. Without this strengthening, the original axioms admit a family of distinct functionals. For the convex integral, we derive a representation as the maximum of ordinary integrals over additive measures dominated by the capacity and establish parallel axiomatic characterizations, with the relevant inequalities reversed relative to their concave counterparts.

Scholarly evaluation must reconcile two imperfect signals: the ex-ante judgment reflected in journal prestige and the ex-post impact measured by citations. We develop a unified axiomatic framework that integrates an ordinal journal list with cardinal citation counts and characterize two complementary families of ranking rules. Journal-based Bean-Counting rules treat list placement and citations as substitutes or complements through citation thresholds. Citation-based Asymmetric Constant Elasticity of Substitution (CES) aggregators reward publication breadth inside the journal list and citation depth outside it. Applied to 4,722 economists at universities that appeared in the QS Top 100 between 2023 and 2026, the two families produce sharply different rankings across fields, especially in microeconomic theory and economic history. Adjusting for field differences in citation rates leaves the overall clustering structure largely stable, though within-field robustness varies across methods.

We develop a welfare-based concentration index that generalizes the Herfindahl–Hirschman Index (HHI) by incorporating pairwise product interactions. In differentiated-product markets, it adjusts the HHI for the strength and direction of product interactions, raising measured concentration for substitutes and lowering it for complements. Combining the index with aggregate output yields welfare indices whose interaction weights reflect the relative emphasis on consumers versus producers. Merger welfare effects therefore depend jointly on the levels of and changes in concentration and aggregate output. An application to U.S. automobiles illustrates how product interactions affect the assessment of concentration and welfare.

Organizations often construct a single performance score from aggregated rather than detailed data. Aggregated observations can conceal different underlying profiles, whose evaluations depend on both the weights assigned to individual measures and how those measures reinforce or overlap with one another. This creates two distinct design decisions: how to combine detailed measures and how to handle the unresolved detail behind an aggregated score. We organize three established aggregation methods for the first decision and study three treatments for the second: equal splitting, benefit of the doubt (BOD), and penalty of the doubt (POD). Equal splitting evaluates an evenly distributed profile, while BOD and POD select the most favorable and least favorable evaluations consistent with the observed data. Combining these methods and treatments produces a unified nine-rule framework. We characterize the three treatments through principles governing how evaluations respond as information becomes more or less detailed. These characterizations connect each treatment to a distinct information environment: BOD applies when detail is unavailable beyond the entity’s control, POD discourages strategic withholding, and equal splitting applies when performance is inherently measured only in aggregated form. They also reveal that, when measures have different weights, equal splitting is incompatible with either consistently favorable or consistently unfavorable treatment of coarse information. Applying the framework to MSCI ESG ratings for 1,257 firms, we find that the treatment of unresolved detail affects score levels more than the choice of aggregation method in most industries, while coarsening changes firm rankings more than interactions among measures do, on average.