The most beautiful daughter of a high-society family, Aglaya is spoiled, intelligent, and unhappy with the idea that she must marry for social status. She spends the novel trying to understand her feelings for Myshkin and to decide whether or not to marry him instead of a more appropriate suitor.
It's a pretty old trick to set up two characters in a compare-and-contrast sort of deal in a novel. Think about two those sisters from "Goblin Market," or Becky and Amelia from Vanity Fair, or of course the Danny DeVito and Arnold Schwarzenegger characters from Twins. And it makes sense that this old standby comes up again and again—it's just a really easy way for an author to do a "show, don't tell" for whatever quality he wants to examine. This way, instead of moralizing via the narrator, which tends to be pretty boring, an author get to just say, "we're just going to conduct an experiment here."
Check out exhibit A, all schemes and lies and manipulation, and his friend, exhibit B, all truth and feelings and moral fiber. Who do you think is going to do well? And then, depending on whether what we're reading is a satire or a comedy or a tragedy or whatever, the appropriate character will come out on top. And before you know it, you've got yourself a text with a point.
So, in a lot of ways, that's what we have going on in The Idiot with Aglaya. She is just fundamentally the anti-Nastasya. She was born in a good, wealthy family; her parents love and shelter her; and her prospects for life are pretty much rosy. We are definitely meant to look at her next to Nastasya and really scratch our heads about Myshkin's inability to decide.
But you know how with Nastasya, Dostoevsky takes a stereotypical character and tweaks it? Well, it seems like it's the same deal here. After all, Aglaya doesn't actually have many of the qualities that would make her Nastasya's opposite. And we get a giant honking signal about just that early on in the novel.
Remember what happens when Myshkin gets a load of Nastasya's portrait? (If not, check out Shmoop's "Nastasya" section for a refresher.) Well, just after that, Myshkin meets the Epanchin family and does a weird thing where he tells him all about their faces. All except that Aglaya that is. Her mom corners him about it and he says:
"You are very beautiful, Aglaya Ivanovna, so beautiful that one is afraid to look at you. […] It is difficult to judge when such beauty is concerned. I have not prepared my judgment. Beauty is a riddle."
"That means that you have set Aglaya a riddle!" said Adelaida. "Guess it, Aglaya! But she's pretty, prince, isn't she?"
"Most wonderfully so," said the latter, warmly, gazing at Aglaya with admiration. "Almost as lovely as Nastasia Philipovna, but quite a different type." (1.7.8-12)
Bam! From the horse's mouth.
But don't just take Myshkin's word for the idea that Nastasya and Aglaya are flip sides of the same coin. There are other clues. For one thing, Aglaya is not nearly as sexually or psychologically innocent as everyone around her would like to believe. Remember how she suddenly busts out with the fact that she knows that Myshkin and Nastasya lived together—and that, as any sane person would, she assumes that he must have been hitting that? Remember just how perceptively accurate Aglaya's description of Nastasya is during that climatic meeting when they call each other out? She says,
"I was sorry for [Myshkin] because he, in the simplicity of his soul, believed that he could be happy with a woman of your character. What I feared actually took place; you could not love him, you tortured him, and threw him over. You could not love him because you are too proud—no, not proud, that is an error; because you are too vain—no, not quite that either; too self-loving; you are self-loving to madness. Your letters to me are a proof of it. You could not love so simple a soul as his, and perhaps in your heart you despised him and laughed at him. All you could love was your shame and the perpetual thought that you were disgraced and insulted. If you were less shameful, or had no cause at all for shame, you would be still more unhappy than you are now." (4.8.117)
Boy, that is really right on the money.
For a third thing, don't Aglaya and Nastasya have pretty much the same personality? They are both really sharp, sarcastic, kind of obnoxious, and also both totally insecure and unable to figure out how to deal with themselves.
And, as the final cap on this train of thought—consider just what Nastasya thinks about Aglaya, as we learn from all those letters she sends her. All that stuff about Aglaya being a creature of pure light or whatever? That kind of strikes us as the wishful thinking of the "there but for the grace of God go I" variety. Maybe we're wrong, but it seems like Nastasya actually sees Aglaya as what she could have been with a different start in life, and not so much as a diametric opposite.