To put it mildly, this is not really a desiderata at all, it’s actually an extremely baffling property.
How can we decide an axiom used to pin down a bargaining solution is intuitive or baffling without first having a goal in mind? Which axioms are sound for the bargaining solution used to pick deals depends on the purpose that led us to want to apply bargaining theory to a problem. If you’re designing a file sharing protocol, you don’t care about bargaining chips. You just want the files to be distributed quickly. Or if you’re designing a standard for network equipment and you want to minimize spectrum congestion or wireless interference, knowing that you can’t trust the owners of the equipment not to be selfish at the expense of other users. You want the solution that works best and if some solution that isn’t the solution that works best becomes unavailable, that doesn’t change the solution you consider best. Independence of irrelevant alternatives is sound for some of the goals we want to apply bargaining theory to.
How can we decide an axiom used to pin down a bargaining solution is intuitive or baffling without first having a goal in mind? Which axioms are sound for the bargaining solution used to pick deals depends on the purpose that led us to want to apply bargaining theory to a problem. If you’re designing a file sharing protocol, you don’t care about bargaining chips. You just want the files to be distributed quickly. Or if you’re designing a standard for network equipment and you want to minimize spectrum congestion or wireless interference, knowing that you can’t trust the owners of the equipment not to be selfish at the expense of other users. You want the solution that works best and if some solution that isn’t the solution that works best becomes unavailable, that doesn’t change the solution you consider best. Independence of irrelevant alternatives is sound for some of the goals we want to apply bargaining theory to.