Normalisation procedures: if they are 'structural' (not caring about details like the names of the theories or outcomes), then the two theories are symmetric, so they must be normalised in the same way. WLOG, as follows:

T1(A) = 2, T1(B) = 0, T1(C) = 1, T1(D) = 0 T2(A) = 0, T2(B) = 1, T2(C) = 0, T2(D) = 2

Then letting q = (1-p) the aggregate preferences T are given by:

T(A) = 2p, T(B) = q, T(C) = p, T(D) = q

So:

• if p > 2/3, the aggregate chooses A and C
• if 1/3 < p < 2/3, the aggregate chooses A and D
• if p < 1/3, the aggregate chooses B and D

The advantage of this simple set-up is that I didn't have to make any assumptions about the normalisation procedure beyond that it is structural. If the bargaining outcome agrees with this we may need to look at more complicated cases; if it disagrees we have discovered something already.