Jigsaw: You think it's the living who have the ultimate judgment over you, because the dead have no claim over your soul. But you may be mistaken.
Jigsaw: Hello, William. Before you are six of your most valuable associates. The ones who find errors in policies. Their findings result in over two-thirds of all applications denied or prematurely terminated. Healthcare decisions should be made by doctors and their patients, not the insurance company. Six ride the carousel, but only two can get off. The decision of which two survive falls upon you. To offer the two reprise, you'll offer a sacrifice of your own. Two can live, four will die.
Jigsaw: Once you see death up close, then you know what the value of life is.
Chosen answer: The trap wouldn't have worked if William stood on the other side of the cage. When William walks towards the mother and son, you see a closeup of his feet stepping onto a pressure-pad that activates the trap. If William stood on the other side of the cage, the trap would never have turned on because the pressure-pad would not have been set off, and nobody would have died. Also, even though Jigsaw pre-plans his traps, there certainly are circumstances where the mother and son could have gotten hurt. One must remember, Jigsaw is insane, and it's shown repeatedly in the series that even though he intends to help people, he is not above sacrificing people or putting innocent people in harm's way to teach his subjects a lesson. (The most prominent examples being the mother and daughter from the original film and Joyce from "Saw 3D" who were innocent but placed in direct danger to be a motivation for the subjects).