In the Shuttle they would use command averaging. All four computers would get access to an actuator which would tie into a manifold which delivered power to the flight control surface. If one disagreed then you'd get 25% less command authority to that element.
> In the Shuttle they would use command averaging
I think the Shuttle, operating only in LEO, had more margin for error. Averaging a deep-space burn calculation is basically the same as killing the crew.
Sure, but these maneuvers aren't done realtime and aren't as time-sensitive; a burn is calculated and triple checked well in advance. If there was an error, there's always time to correct it.
In the case of moon landings, the only truly time-critical maneuvers are the ones right before landing... and unfortunately, a lot of fairly recent moon probes have failed due to incorrect calculations, sensor measurements, logic errors, etc.
The GNC loop runs several times per second. The desired output will consequently be increased by the working computers to achieve the target. The computer does not "dead reckon" anything.
Travelling through Max-Q in Earth atmosphere on ascent is far more dangerous.
> Travelling through Max-Q in Earth atmosphere on ascent is far more dangerous
Fair enough. I don't know enough about Orion's architecture to guess at propellant reserves, and how life-or-death each burn actually is.