As Myshkin's competitor for Aglaya's hand in marriage, Radomsky is a far more socially appropriate suitor, although she does not actually love him.
Radomsky is another character who kind of seems—well, not in-the-way exactly, but just…. Why is he in the novel? Is he necessary? A few parts of the plot kind of half-heartedly involve him, but mostly he falls by the wayside and his presence is never really explained. If we were making this into a movie, he's the guy whose role would end up on the cutting room floor. Let's see. First, there's the competing-suitor plot line that could have potentially made him a big star, but the novel isn't really about whether Aglaya will follow her heart or her head, so this is pretty much a nonstarter for him from the get-go.
Then there is the odd plot line of Radomsky as a schemer or plotter, when he has something mysterious to tell the prince but never does, or when he has some secretive thoughts about Ippolit that get hinted at but never told. All of that stuff just gets a big "Huh?" from us because it is never really developed. Finally, at the end, there is the conversion plot line, where Radomsky is so moved by the prince that he ends up caring for him abroad. Well, maybe, but because we never have much insight into what Radomsky is thinking or experiencing at any given moment, there doesn't seem to be much of an arc to get him from point A (no belief) to point B (belief).
What do you think? What is the purpose of this character? What does he accomplish? How would the novel be different without him?