  The expectation and the mean of partitions generated by a cluster ensemble
are not unique in general. This issue poses challenges in statistical inference
and cluster stability. In this contribution, we state sufficient conditions for
uniqueness of expectation and mean. The proposed conditions show that a unique
mean is neither exceptional nor generic. To cope with this issue, we introduce
homogeneity as a measure of how likely is a unique mean for a sample of
partitions. We show that homogeneity is related to cluster stability. This
result points to a possible conflict between cluster stability and diversity in
consensus clustering. To assess homogeneity in a practical setting, we propose
an efficient way to compute a lower bound of homogeneity. Empirical results
using the k-means algorithm suggest that uniqueness of the mean partition is
not exceptional for real-world data. Moreover, for samples of high homogeneity,
uniqueness can be enforced by increasing the number of data points or by
removing outlier partitions. In a broader context, this contribution can be
placed as a further step towards a statistical theory of partitions.
