It seems that half of the drivers out there these days do not know what to do at a 4 way intersection. (Law & Order da-da sound). These are their rules.
1) Step on the gas as you approach a 4-way stop. As you prepare to yield at the stop sign, scope out the competition. Notice if there are any cars at any of the other stops, or if there are any approaching at the same time.
2) Sporadically apply the gas and brake to let the competition know that you mean business. Notice if there is something blocking your view in the cross walk lines. Determine if you will miss the object or just clip them in a harmless tag "you're it" sort-of-way.
3) Look to see if the other three cars have come to a complete stop. If so, then lay on the gas and let 'er rip. If you don't get hit, you've found an excellent way to prolong the life of your brakes.