[Pat Fairbank]

I think the fairest system, and the one requiring the least amount of work to implement, is the one that many teams (including my own) try to follow now -- you show up early in the morning with as many people as seats you want to claim, and stand in line.

Where this fails right now is that there is often not a clear indication of where the line starts (i.e. which door(s) will be opening) and no effort to enforce that teams respect the line (other than teams' GP, which sadly often goes missing at this point in the competition). This is easily and inexpensively solved with signage and crowd control barriers.

Edit: Having one such line for each division, at its own set of doors at the four corners of the dome, would also go a long way towards decreasing the safety hazard of people pushing or running in different directions after they get in.