In most sections, you now have the option of marking topics self-moderated when creating them. In self-moderated topics, the OP can delete replies. The option for enabling this is under "additional options". Topics cannot be converted to self-moderated topics after creation.
There are no rules to self-moderation. In self-moderated threads, replies belong to the OP. In other threads, replies belong to the respondents individually. Think carefully about whether you want to reply to a self-moderated topic, as your post may not be given due respect.
Tell me if there are any bugs. If this ends up not working out well, I might remove it.