Originally Posted by bubbers44
[...] does the computer average the two opposite inputs?
Their inputs are added (limited to full deflection of a single stick), not averaged. This form of cross-controlling is strictly discouraged, but possible. There are indications on the glareshield, as well as an aural warning: "DUAL INPUT".
When he selects priority on his side does it disengage from the averaging of the two side sticks to full authority on the left side stick?
Yes. The other stick is then ignored. This is the SOP for taking over control, along with announcing "I have control", or whatever wording your airline prescribes.
Bernd