Basically all tickets would naturally migrate to P4. Eventually when someone started working on 'the wrong thing' another level was added.
In my current job we use Jira and the backlog has things at the bottom which have been just added, things at the top which we thought were priorities at some point and a whole bunch of crap in the middle which is unordered.
I keep thinking about some kind of system where people would rate the priority of one ticket against each other rather than against an arbitrary scale.