A Measure of Insufficient Performance

This paper introduces and characterises a measure of insufficient performance that is decreasing and convex with respect to deviations from a minimal threshold. The measure is defined as the logarithm of the geometric mean of these deviations, weighted by the relative frequency of faulty outcomes. Our measure exhibits an elementary mathematical structure, is easy to interpret, and satisfies some desirable properties, such as scale independence, replication invariance, and decomposability by observational subgroups. We provide two illustrations on the applicability of this evaluation protocol, regarding the labour market and life satisfaction.