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Many Artificial Intelligence tasks cannot be evaluated with a single qualitycriterion and some sort of weighted combination is needed to provide systemrankings. A problem of weighted combination measures is that slight changes inthe relative weights may produce substantial changes in the system rankings.This paper introduces the Unanimous Improvement Ratio (UIR), a measure thatcomplements standard metric combination criteria (such as van Rijsbergen'sF-measure) and indicates how robust the measured differences are to changes inthe relative weights of the individual metrics. UIR is meant to elucidatewhether a perceived difference between two systems is an artifact of howindividual metrics are weighted.  Besides discussing the theoretical foundations of UIR, this paper presentsempirical results that confirm the validity and usefulness of the metric forthe Text Clustering problem, where there is a tradeoff between precision andrecall based metrics and results are particularly sensitive to the weightingscheme used to combine them. Remarkably, our experiments show that UIR can beused as a predictor of how well differences between systems measured on a giventest bed will also hold in a different test bed.

Combining Evaluation Metrics via the Unanimous Improvement Ratio and its Application to Clustering Tasks