What was the arena built for in "The Lady or the Tiger?" by Frank Stockton?

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The king in this story is described as "semi-barbaric," meaning that he is, in his essence, barbaric by nature, but has borrowed some more civilized ideas from some of the gentler nations which surround his kingdom. The public arena which he builds is actually, in its origin, one of these "borrowed notions" intended to reduce the barbarism of the nation by offering a space to display exhibitions of valor, which would supposedly refine and culture his subjects.

However, being at heart a barbaric king, the king warped this idea in the arena which he built. He doesn't have any interest in showcasing gladiators or religious people fighting with tigers in the hopes of improving their minds this way, as the Romans did. Instead, he prefers to use his vast amphitheater as an "agent of poetic justice," used for punishing crimes and rewarding virtues based on chance alone. When an interesting enough crime was committed, the fate of the supposed criminal would be decided in the king's arena.

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The king's arena in Frank Stockton's short story "The Lady or the Tiger?" was a "vast amphitheater" built in order to deliver the king's justice. It was large enough to house the king's subjects, "encircling galleries," "mysterious vaults," and "unseen passages." The king believed his arena was the agent of an "incorruptible" justice. When someone was accused of a crime, they were taken to the arena, where their judgment was in their own hands. They were given the choice of two doors. One of the doors would reveal a tiger, which promptly killed the accused and rendered him guilty. Behind the other door was a lady who "immediately" married the accused because, by choosing so judiciously, he had proven his innocence. The narrator refers to it as "poetic justice" because the accused could never know from which door might spring the tiger or the lady. Unfortunately, like all things supposedly incorruptible, the justice of the arena becomes corrupted when the king's daughter discovers the secret of the doors.

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