Normally, both sidesticks are prioritized equally and simultaneous input is added. While one pilot keeps their priority takeover pushbutton pressed, the other sidestick is completely deactivated. There is no "more effective" logic, it will ignore all inputs from the other stick (this refers to moving the stick, the buttons on the stick are still functional). Momentarily pressing the priority takeover button without holding it, will only deactivate the autopilot, but not result in any priority change.
The FCOM contains the full details:
Sidestick priority logic
- When only one pilot operates the sidestick, it sends his control signals to the computers.
- When the pilots move both side stick simultaneously in the same or opposite direction and neither takes priority, the system adds the
signals of both pilots algebraically. The total is limited to the
signal that would result from the maximum deflection of a single
sidestick.
Note: In the event of simultaneous input on both sidesticsk (2° deflection off the netural position in any direction) the two green
SIDE STICK PRIORITY lights on the glareshield come on and "DUAL
INPUT" voice message is activated.
A pilot can deactivate the other sidestick and take full control by
pressing and keeping pressed his priority takeover pushbutton. For
latching the priority condition, it is recommended to press the
takeover push button for more than 40 seconds. This allows the pilot
to release his takeover push button withou losing priority. However, a
pilot can at any time reactivate a deactivated stick by momentarily
pressing the takeover push button on either stick. If both pilots
press their takeover pushbuttons, the pilot that presses last gets
priority.
Note: If an autopilot is engaged, the first action on a takeover pushbutton disengages it.
In a priority situation:
- A red light comes on in front of the pilot whose stick is deactivated.
- A green light comes on in front of the pilot who has taken control, if the other stick is not in the neutral position (to indicate a
potential and unwanted control demand).
(Airbus A320 FCOM - Flight Controls - Controls and Indicators)
This logic likely has not changed in any subsequent fly-by-wire Airbus aircraft. The A380 FCOM has a different description, but the general logic seems to be the same:
SIDESTICK PRIORITY LOGIC
At all times, only one flight crewmember should fly the aircraft.
However, if both flight crewmembers use their sidesticks
simultaneously, their orders are algebraically added.
The flight
control laws limit the combined order to the equivalent of the full
deflection of one sidestick.
A flight crewmember can deactivate the
other sidestick and take full control, by pressing and keeping pressed
the sidestick pb.
If a flight crewmember presses their sidestick pb
during 30 s, the other sidestick is permanently deactivated, until any
flight crewmember presses their sidestick pb.
If both flight
crewmembers press their sidestick pb, the last pilot to press gets the
priority.