Many different relative clustering validity criteria exist that are very useful in practice as quantitative measures for evaluating the quality of data partitions, and new criteria have still been proposed from time to time. These criteria are endowed with particular features that may make each of them able to outperform others in specific classes of problems. Then, it is a hard task for the user to choose a specific criterion when he or she faces such a variety of possibilities. For this reason, a relevant issue within the field of cluster analysis consists of comparing the performances of existing validity criteria and, eventually, that of a new criterion to be proposed. In spite of this, there are some conceptual flaws in the comparison paradigm traditionally adopted in the literature. The present paper presents an alternative methodology for comparing clustering validity criteria and uses it to make an extensive comparison of the performances of 4 well-known validity criteria and 20 variants of them over a collection of 142,560 partitions of 324 different data sets of a given class of interest.