Yes, I think we need something like this veil of ignorance approach.

In a paper (preprint) with Ord and MacAskill we prove that for similar procedures, you end up with cyclical preferences across choice situations if you try to decide after you know the choice situation. The parliamentary model isn't quite within the scope of the proof, but I think more or less the same proof works. I'll try to sketch it.

Suppose:

• We have equal credence in Theory 1, Theory 2, and Theory 3
• Theory 1 prefers A > B > C
• Theory 2 prefers B > C > A
• Theory 3 prefers C > A > B

Then in a decision between A and B there is no scope for negotiation, so as two of the theories prefer A the parliament will. Similarly in a choice between B and C the parliament will prefer B, and in a choice between C and A the parliament will prefer A.