The first part of this sounds very closely related to something called Rogerian argument [1] which aims to find new opportunities for consensus by building on views already held in common.
The bit about assigning probabilities is interesting, precisely because I can think of very few contexts in which it would be of use to me. People seem to have little tolerance for shades of uncertainty when expressing views, whereas privately we think in probabilities all the time. It's as though we play a kind of poker where our need to conserve our 'stack' of reputational authority makes us relegate the actual ideas in contention to mere 'hands' to be represented, bluffed, and trivially discarded when a more amenable certainty presents itself.
The bit about assigning probabilities is interesting, precisely because I can think of very few contexts in which it would be of use to me. People seem to have little tolerance for shades of uncertainty when expressing views, whereas privately we think in probabilities all the time. It's as though we play a kind of poker where our need to conserve our 'stack' of reputational authority makes us relegate the actual ideas in contention to mere 'hands' to be represented, bluffed, and trivially discarded when a more amenable certainty presents itself.
[1] https://en.m.wikipedia.org/wiki/Rogerian_argument#Rapoport's...