DC-ATE, from answers posted previously by those who know, if the two side sticks are sending different messages, and nobody pressed the priority button, the aircraft takes the average.
If one pilot presses the button, that takes priority. If the other one then presses his/hers, it reverts to that one.
Apparently the intention was to enable one to take over if needed, not to resolve a tug of war between two pilots who refuse to agree.
At one point, PNF Robert pressed his and announced that he was taking it. Shortly after, Bonin took it back, with no such announcement, and it stayed that way.
AIUI.
Chris N