Why on earth would you want 'arithmetic summation' of both sidesticks ?
Because both sidesticks are not connected and this makes it intuitive for the other pilot to make/add corrections. Eg trainee does not pull enough in the flare. LTC's sidestick is neutral. He just wants to add a bit of nose up so he just pulls his stick a bit and his input is added to that of the trainee.
If you want to take control regardless of what the other guy is doing, just push the disconnect button to override him...