You are absolutely right. It's not clear from the abstract whether there is a buried absolute comparison. The idea that the average of the group as a whole is r

You are absolutely right. It's not clear from the abstract whether there is a buried absolute comparison. The idea that the average of the group as a whole is raised seems so obvious I didn't even consider a reality where less competent men were replace by even less competent women. Edit (oh look a full text article, I didn't expect to see a link so I assumed it was just an abstract link). What it does say at least is that while the quota removed a fraction of men that turned out to be less competent than those that were removed, thereby improving the average competence of the remaining group of men, the added group of women did not have lower competence than the existing group (which would perhaps have been expected). For women, we obtain a negative coefficient in the regression specification without municipality trends, but a positive coefficient with trends. In neither case, however, is the estimate significantly different from zero, suggesting that the quota neither raised nor cut the share of competent women. This is interesting in view of the meritocratic critique of gender quotas, namely that raising the share of women through a quota must necessarily come at the price of lower competence among women. Since men and women aren't compared in absolute terms, this doesn't mean there was an increase in competence either. But it does say that it wasn't a replacement of the group of low competence men (compared to their peers) with a group of low competence women (compared to their female peers). So that does suggest something (which the article does note), for example that the pool of competent women could be larger.