In Persuasion does the aristocracy perform any useful social functions? What is aristocracy's role in society?
Jane Austen, through her characters, makes some rather indirect conclusions about aristocracy and the unfair role that she felt they held in society. Being an aristocrat did not make you a good human being; you could be good, but just because you were a duke or a noble didn't not mean you deserved the respect that society gave you.
The main role that Austen shows the aristocracy playing is that of touting their names and stations in life in order to gain power, money and form alliances based solely on power and money. If you are a duke, then that is all that matters as far as being respected goes, and attaining the title of a duke is well worth manipulating, hurting and scamming those around you. The main character that this is seen through is William Elliot, Anne's conniving cousin who wants to attain riches through her family. To do so, he has to lie, scheme and manipulate all of them into thinking that his character is one of integrity and respectability. In reality, he is a scoundrel, and seeking only for money and power.
In other parts of the novel, the humiliating regard and submissiveness that characters show to the aristocracy really bother Anne; she is embarrassed by her father's behavior towards people simply because they are above him on the social scale, and instead prefers to look to people for their characters and hearts. This is a common theme throughout Austen's works; take for example Pride and Prejudice, where one of the most influential and yet close-minded characters is Lady Catherine, the aristocracy of that novel. Austen seemed to be making the point that titles were no indication of being worthy of respect.
I hope that helped; good luck!