Always resolve inter-party rock-paper-scissors the way I want to?

It seems your second character, in your case Roderick, picks always the same until the left character wins one time. Then the right character shifts one to the left.

When the left character starts with paper and the right one with the scissors, the right one will choose the scissors as long as you choose paper. This way the right char wins the argument. If you switch to stone and thus beat the scissors, the right char will move one symbol to the left. So his choice will be paper the next time. You can now choose the scissors and beat him again. Also he will again move one symbol to the left and choose stone. So you can "go in circles" and win the argument with the left character.