Who is at fault for Piggy's death, Jack or Roger?Was the death of Piggy due to the fact that Jack reigns over the island and his "irresponible...

Roger.

“Roger, with a sense of delirious abandonment, leaned all his weight on the lever.” 

Thus dislodging the boulder that killed Piggy.

You could argue that due to Jack being chief he was in charge and so it’s his responsibility to control the group and so his fault.