In "The Lady or the Tiger", what does the author mean by "when he and himself agreed upon anything, the thing was done"?
Simply put, it means the king answers to no one. He only consults with himself and it only takes he and himself (a literary play on words that means he and he alone) to make a decision. This undoubtedly goes to the barbaric side of his nature. When the author tells us that it is the daughter of the king who makes the decision in "The Lady or the Tiger?" as to who will come out of the door, we may gain insight as to what will be on the other side of the door.
But as Frank Stockton put it, we have to leave that with our noble reader.