On the last 5 pictures yes, all chars had the same authority.
What i've shown is:
If you have a char with 9 auth in the lower branch, and a char with 9 auth in the upper branch, the lower branch gets chosen.
If all chars have 0 auth, the upper branch gets chosen.
So if everyone in both branches have 25yr's old, and 0 auth, the last one from the upper branch gets heir.
If everyone in both branches have 25 yr's old, and 9 auth, the last one from the lower branch gets heir.
So basically:
If the same highest authority value exists in both branches and its above 0, the lower branch takes priority in heir choosing.
If the highest authority value in both branches is 0, the upper branch takes priority in heir choosing.