How does the author show the king is semi-barbaric?
The author shows the king is semi-barbaric by describing his system of "justice." Rather than using facts and evidence to determine whether a person is guilty or innocent of a crime, the king uses a superstitious method that is akin to having a person walk on hot coals. In this case, the person accused of a crime has to choose between two doors. If he chooses the door with the beautiful maiden behind it (the story assumes the accused will be male), he is believed innocent. If he chooses the door with the tiger behind it, he is devoured and assumed guilty.
A death penalty that involves being killed and eaten by a hungry tiger in front of a huge crowd of people is more than a little "semi-barbaric." What makes it worse is that the king finds this a good way to entertain his subjects while at the same administering what he sees as "justice."
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