Time has gone by and you have found yourself to be in a wonderful position. You enjoy a certain privledge in this camp, as the dictator has learned to trust you. Unfortunately, you have never mentioned to the dictator that in the beginning, you were four survivors.
Through his irrationality, he claims this to be treason on the basis of dishonesty towards him, which is punishable by execution, "just so you know."
It looks like the raft never made it elsewhere, and the person you sent away has survived, only to tell the dictator that they arrived on the island with YOU.
The dictator is holding this person captive, and requires that you make a decision to determine who will be executed, or by your choice, simply banished.
Do you fess up? You have it quite good here. Do you want to end it all now by banishing yourself?
Or do you lie? They don't have to even know that you will have determined their fate . . .