  The measurement of progress using benchmarks evaluations is ubiquitous in
computer science and machine learning. However, common approaches to analyzing
and presenting the results of benchmark comparisons of multiple algorithms over
multiple datasets, such as the critical difference diagram introduced by
Dem\v{s}ar (2006), have important shortcomings and, we show, are open to both
inadvertent and intentional manipulation. To address these issues, we propose a
new approach to presenting the results of benchmark comparisons, the Multiple
Comparison Matrix (MCM), that prioritizes pairwise comparisons and precludes
the means of manipulating experimental results in existing approaches. MCM can
be used to show the results of an all-pairs comparison, or to show the results
of a comparison between one or more selected algorithms and the state of the
art. MCM is implemented in Python and is publicly available.
