mP CR(A) > mP CR(B) ⇐⇒ (y − z)((x + y)(x + y) − 2x 3) > 0.

As 0 ≤ x ≤
1 2
, we have 2x 3 ≤ x 2 ≤ (x + y)(x + z). So mP CR(A) > mP CR(B**) if**
and only if **y > z**.

That shows that the stability of the decision is reached if a1 = b1 **for all** a2 and b2 ∈ [0, 1] or by symmetry if a2 = b2 for all a1 and b1 ∈ [0, 1].

4.3.2 Case a1 = b2 In this situation, expert 1 believes A and the expert 2 believes B **with the same**
weight:

![0_image_0.png](0_image_0.png)

![0_image_1.png](0_image_1.png)

Figure 3: Decision changes, projected on the plane a1, b2.

The conjunctive rule yields:
mc(∅) = x 2 + yz, mc(A) = x + z − xz − mc(∅) = −x 2 + x(1 − z) + z(1 − y),
mc(B) = x + y − xy − mc(∅) = −x 2 + x(1 − y) + y(1 − z),
mc**(Θ) = 1 +** mc(∅) − 2x − y − z + x(y + z).

Therefore:
$$m_{c}(A)>m_{c}(B)\iff(x-1)(y-z)>0,$$
as 1 − x ≥ 0:
mc(A) > mc(B) ⇐⇒ **y > z.**

$\lambda=u\lambda>0$