Shockley's Ceiling Shawangunks I was rescued like a princesse.

It's not a great idea to start hauling someone you can't see or communicate with (or lower, for that matter). A 3:1 haul you can set up with what's likely on your harness, is going to in reality be a lot less than 3:1 without any pulleys in the mix, and the mechanical advantage can quickly drop to nothing with rope drag in the system. 

A drop loop assist, assuming your partner is conscious and able, is way more bang for your buck in terms of effort to effect, but it's only possible if your climber is less than 1/3 of the rope length away from you. You lower down a loop of rope to them, keeping hold of the other end, and they clip the loop to themselves with a locking carabiner. They pull down while you pull up, and with your combined efforts and the pulley action they can lift themselves easily. You've got to keep belaying while you do this, if they're on a guide mode or similar belay they can be pulling down on their own brake strand, getting a little extra pulley action and simultaneously capturing their own progress. 

This would also be very difficult without communication, and I wouldn't expect the climber (in this case as described) to know what to do with a drop loop. The first step, (assuming you've already gotten yourself into this situation without teaching your completely new partner what to do) would be to establish communication. I would probably rap down on a separate line rather than prussik the climbers strand, assuming I had enough rope to do so, and would try to set it up so I could establish myself at the lip where I could see and speak with my partner, then try a drop loop assist from there. 

Then again, it's hard to imagine an experienced leader with these skills in their toolbox failing to either teach their partner how to ascend the rope or choose to avoid overhanging climbs with this potential for a fall into open space. So if the leader is as unprepared as the follower, maybe screaming your head off and hoping for the best is the way to go. 

Em Cos wrote:

Then again, it's hard to imagine an experienced leader with these skills in their toolbox failing to either teach their partner how to ascend the rope or choose to avoid overhanging climbs with this potential for a fall into open space. So if the leader is as unprepared as the follower, maybe screaming your head off and hoping for the best is the way to go. 

Most accurate statement ever.