I went back and added the "between trusted allies/partners" because the sentence didn't seem true without it - it overgeneralized you in ways that didn't seem right (hah!) and also overgeneralized our differences into places that we're less different. :)

if I think the unfairness is in my favor, then I get nervous because I have no idea where the tipping point is

For me, at least, this is self-correcting. If I don't care as much about where to go to dinner (my classic example), and concede to go to the place you want to go, that's all good. If every time we go to the place you want to go, then at the point at which that starts to bug me, then that's also exactly the point at which I care more that we go to the place I want to go, so I push harder for my place rather than starting out by conceding. Assuming that you are using the same negotiation protocol as me, then you concede when I care more and we go to my place as much as is necessary to keep me from hitting the tipping point.

I suppose that this might make me seem erratic in things like "how much do I care about this sort of thing" but the whole protocol fails if one can't make a reasonable job of both perceiving and conveying how much both parties care about the things being negotiated.