I think randomness is an underrated tool for introducing a sense of “fairness” to problems with strange power dynamics: where everyone is interested in a fair outcome, but the best outcome for any individual causes some harm to the group.
Salary negotiation is one example. Imagine haggling over the range start or range size, and then picking your salary from a uniform distribution contained by that range. I wonder how the distribution of (un-)satisfactory outcomes of this system that would compare to the one we have today.
It’s also interesting to note certain parallels to structures existing today. The group stage draw for the UEFA Champions League comes to mind.