What is the significance of the fact that General Zaroff sings a tune from Madame Butterfly after Rainsford jumps off the cliff?
I don't think that this means the allusion; I think it's talking about symbols or themes or something....if you can answer this it'd help a lot :)
This is a very interesting question! I'm not sure that I have the answer you're looking for, but I think that one aspect of the plot of Puccini's Madame Butterfly might be significant.
Though the opera's story is somewhat complicated (and much of it isn't relevant for your purposes), in a nutshell, it's about a Japanese woman (Butterfly) and an American soldier (Pinkerton) who get married and who live atop a hill--or cliff--overlooking the city and the bay. The cliff is significant, as the journey to the top of it is difficult, yet Butterfly insists that more difficult is the anticipation of seeing her husband. At the beginning of the opera, the cliff is significant, because it represents Butterfly's happiness.
However, Pinkerton returns to America, leaving Butterfly in Japan for a few years, and refusing to acknowledge that Pinkerton might not want to come back for her, Butterfly fantasizes that she is on the top of a cliff and sees her husband's ship coming toward her. She says she won't go down the cliff to meet him, but that he will come to her.
Pinkerton does return, eventually, but it is with his new American wife, Kate. Butterfly becomes so distraught that she commits suicide so that the child she bore years earlier with Pinkerton may go to America with him and his new wife and have a better life. Thus, the cliff, which was once a place of joy and hope, becomes one of tragedy. (Just as, perhaps, Zaroff hopes the cliff on Ship-Trap Island will become for Rainsford.)
In "The Most Dangerous Game," it's probable that Connell's knowledge of Puccini's opera--and its setting--gave him the idea for what is certainly a subtle yet complex allusion to Madame Butterfly.
As I said before, I'm not sure if this is the information that you're looking for. But I hope it helps!
I do not think that it the actual piece that Zaroff is humming from matters. What does matter is that he is humming a bit of an opera by a famous composer. The reason that this matters is that it adds to the image of Zaroff that we have -- he is always portrayed as this guy who is trying to act all civilized and high class.
Through the story, Zaroff shows that he feels that he is part of the elite. That is part of why he hunts people -- he feels he's just better than them. By humming bits from an opera (and then by going and having fancy food after), Zaroff is showing that he sees himself as this cultured elite type.
This matters because his attitude is in complete contrast with the uncivilized thing that he is doing. It makes him seem hypocritical -- he feels that he is better than everyone else but he is doing this horrible thing that no one else would think was acceptable.