Include yellow and red cards in the amenity packs. Passengers can hold them up during the flight to let the crew know how they're doing. If more than 50% of passengers in any one cabin show a red card, the crew are sent off and passengers continue with self-service.

What can possibly go wrong?

If BA's IT was any good, i'd say the could also allow passengers to vote via the IFE, but that would rule out its use on 10-20% of flights.