The history of life shows a clear trend in hierarchical organization, revealed by the successive emergence of organisms with ever greater numbers of levels of nestedness and greater development, or ‘individuation’, of the highest level. Various arguments have been offered which suggest that the trend is the result of a directional bias, or tendency, meaning that hierarchical increases are more probable than decreases among lineages, perhaps because hierarchical increases are favoured, on average, by natural selection. Further, what little evidence exists seems to point to a bias: some major increases are known – including the origin of the eukaryotic cell from prokaryotic cells and of animals, fungi and land plants from solitary eukaryotic cells – but no major decreases (except in parasitic and commensal organisms), at least at the cellular and multicellular levels. The fact of a trend, combined with the arguments and evidence, might make a bias seem beyond doubt, but here I argue that its existence is an open empirical question. Further, I show how testing is possible.