And the second? And the third?The party with the most total of votes in the district gets to choose the 1st name.
If there were no sectarian or caza quotas, having the party decide the order works because all seats are basically equal. But with the quotas, it becomes harder. There could be some sort of highest averages method but those have their problems as well and tend to favor larger parties. I think that the preferential votes are a fair way to gauge which candidates are most deserving of their seats, i.e. having the highest support from the local voters.