  Many Artificial Intelligence tasks cannot be evaluated with a single quality
criterion and some sort of weighted combination is needed to provide system
rankings. A problem of weighted combination measures is that slight changes in
the relative weights may produce substantial changes in the system rankings.
This paper introduces the Unanimous Improvement Ratio (UIR), a measure that
complements standard metric combination criteria (such as van Rijsbergen's
F-measure) and indicates how robust the measured differences are to changes in
the relative weights of the individual metrics. UIR is meant to elucidate
whether a perceived difference between two systems is an artifact of how
individual metrics are weighted.
  Besides discussing the theoretical foundations of UIR, this paper presents
empirical results that confirm the validity and usefulness of the metric for
the Text Clustering problem, where there is a tradeoff between precision and
recall based metrics and results are particularly sensitive to the weighting
scheme used to combine them. Remarkably, our experiments show that UIR can be
used as a predictor of how well differences between systems measured on a given
test bed will also hold in a different test bed.
