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"?
You would use 'poorest half' where you are looking to emphasise poverty, whereas you would use 'poorer half' where you are merely looking to indicate which half of a 50/50 split your are referring too. It is a subtle difference, but subtlety is what makes a language.
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.