In The Republic, why does Glaucon tell Plato the story of the "Ring of Gyges?"
The "Ring of Gyges" story is a sort of thought experiment. It occurs in the context of a discussion about justice in which Thrasymachus has just argued that, essentially, justice is whatever is in the interest of the strong. Socrates has forced Thrasymachus to reluctantly retreat from this position, and Glaucon takes up the argument with his story of the ring. In short, the ring of Gyges has the power to make its wearer invisible. When Gyges, an honest shepherd, finds the ring, he almost immediately begins to act in ways he would not have done previously. In particular, he conspires to seduce the queen and overthrow the king, seizing the kingdom for himself.
In telling this story, Glaucon is arguing that men behave in just ways not because they are inherently just, but because they will face consequences for behaving unjustly:
No man would keep his hands off what was not his own when he could safely take what he liked out of the market, or go into houses and lie with any one at his pleasure, or kill or release from prison whom he would, and in all respects be like a God among men . . . And this we may truly affirm to be a great proof that a man is just, not willingly or because he thinks that justice is any good to him individually, but of necessity, for wherever any one thinks that he can safely be unjust, there he is unjust.
Glaucon is suggesting that if people calculate that they can get away with doing injustice, they will, because if all external restraints were removed, it would be better for people as individuals to behave in this way. People behave justly or unjustly according to the relative benefits of each type of behavior. Gyges was an honest man before acquiring the ring, not because he was inherently good, but because he was not in a position to behave unjustly. Once he was given the power afforded by anonymity, he became greedy and scheming. Socrates disputes this assertion, but the principle argued by Glaucon in this passage became a fundamental one in Western thought. We can see it in Machiavelli's The Prince, in Leviathan by Thomas Hobbes, and even in Federalist No. 51 by James Madison.
"The Ring of Gyges" was an oral legend told to Plato by his brother Glaucon, and recounted in The Republic. The story concerned a magic ring that made its wearer invisible; this allowed the shepherd Gyges to seduce the Queen of Lydia and assume power after killing the King. The story is an example of a morality tale; the question is whether the power of anonymity would eliminate morality and ethics in any person, even one of very strong moral beliefs. Glaucon argued that two men with opposing moral views would be affected in different ways; the fully honest man would not use the ring's power for his own gain and so would be miserable, while the fully dishonest man would use the ring and be happy and fulfilled.
"If you could imagine any one obtaining this power of becoming invisible, and never doing any wrong or touching what was another's, he would be thought by the lookers-on to be a most wretched idiot, although they would praise him to one another's faces..."
(Plato, The Republic)
The moral of the story is that power will cause any man, even an honest one, to become dishonest, or at least motivated by selfish desires. Glaucon's comment that a person who never used the ring selfishly would be mocked behind his back is interesting, as it seems that those mockers would be fearful of retribution if they spoke aloud even though the ring-bearer never used the ring badly. This speaks to the flawed nature of human moral philosophy; most ethical questions can be confused with semantic arguments and excuses.