I saw the phrase "poorest half of the population." Is superlative always used with "half"? Is "poorer half" okay? Do you also say the "richest half"?
I would say the comparative is traditionally preferred if you're only comparing two things, which is always the case with halves. So I would use the poorer half, at least in formal or literary English. The poorest half, however, is probably also used, and it will probably be immediately clear to readers what it's supposed to mean.
They both sound quite natural to me. It looks like "poorer "half" was much more common in the early 20th century, but both forms seem to appear: Google Ngrams.