Another option would be to choose the team on who you just "like the most". Maybe this would have been more to your liking? It's more human, I guess. However, notice that there is still a criteria and still an evaluation phase, you can't avoid it (unless you pick by random).
None of this means that you have to use text-to-speech and have the computer read out the list of names who were fired. You can still go to each team member and talk about it, like a human.