Assuming that your 4-way stop intersections are lightly traveled like mine, what I will generally do when faced with this situation is immediately turn right. If I am at six o'clock and the driver is at three o'clock, this allows me to slip in behind him and I have not had to stop at all. I then just follow him through the intersection (if my destination route is nine o'clock) or turn right again for a twelve o'clock destination route.

Obviously this works all the way around the clock - it gives the driver/drivers at the other points in the intersection a clear signal they I don't need to account for me in going through the intersection, keeps me moving at a faster rate than stopping and playing the "after you" game, and, most importantly, allows them to get back to their texting and phone calls with a minimum of delay.