What force does a window washer want acting on him when trying to keep the same position

The force he applies on himself is balanced force.

Explanation: Balanced force means the net forces applied on himself will be zero. Which is forces applied on right side will be equal to left side forces. And upward forces will be equal to downward forces. According to first law of motion, an object in rest can never be in motion except some force is exerted on it to do so. Hence if force on window washer will be balanced force (Net force = 0), then there will be no motion and he will be in same position.

That would be balanced.