Background -- as a discipline, we've always had a seniority based system for choosing classes. I'm #2, so it's been to my advantage to keep it -- but, there is something problematic -- in that all four of us could be at BNCC for the next 20 years -- and thus, the #4 guy could get the schedule leftovers for 20 years... As it is, there isn't a significant gap between #1 and #4 -- maybe a total of 9 years... so, the #4 has grounds for complaint.
The standard alternative is to rotate who chooses first. This is problematic as the #1 and #2 folks do almost all of the administrivia -- and that isn't going to change, as the college won't adjust. So, then the #1 and #2 do extra work because they're senior. That kind of sucks. As a discipline, we aren't big enough to have our own chair (I'm the humanities department chair), with release time etc... so that alternative isn't good either.
We started discussing this last spring -- and agreed that the next schedule we'd try a collaborative way of making it work. We'd all come in with two first choices for classes. If there was a conflict, we'd resolve it by seniority -- which seemed to make sense and give a bit of help to #1 and #2. Then we took turns choosing classes in a rather random pattern. Mostly folks selected one or two classes at a time -- depending on how the sections worked together. We made some adjustments and cooperated to make it all work out -- and we each ended up with schedules we could live with. We also spent some effort to make sure that our adjuncts could have decent schedules.
This could have been ugly folks -- really ugly. I can say that I'm lucky and blessed to have colleagues who are genuinely interested in the welfare and happiness of the group.