Armie Hammer did not receive an Oscar nomination for portraying Cameron and Tyler Winklevoss in The Social Network.
The two are proper representations of privilege in every sense, and there is an inherent danger in playing such a type of character, particularly in an Aaron Sorkin screenplay, to veer towards caricature if the actor is not careful. This is not due to underdevelopment of characters in Sorkin's writing rather in his dialogue which is as treacherous as it is rich given its often flamboyant nature. There is almost this idea of Sorkinese which in the wrong hands can easily sound ridiculous and overwritten if not delivered properly. Hammer has a particular challenge there then in that he's already depicting an often simplified type of character with dialogue that could potentially exacerbate this. Hammer wholly avoids this while also making Sorkin's dialogue sing like few other actors have. Hammer in both performances is a master of every little colorful flourish by so effectively realizing the style of both men as natural to these words, and just delivering the lines so well. Hammer perhaps gives the funniest performance, or performances, in the film by making the most out of every line while also by having just the right type of fun with these very particular sort of men.
Now as amusing as Hammer is when pondering between the Winklevi if Zuckerberg offended one of their girlfriends or scoff at the the Prince of Monaco he's careful not to become two caricatures walking around. This is perhaps best seen through the ways he does distinguish the two twins from one another in nuanced and pivotal ways that actually helps to take them beyond simple figures of entitlement. Hammer portrays Cameron and Tyler differently in their personal styles that attaches to their personal belief in their use of that entitlement, however that isn't to say that is all there is to them or to Hammer's performance. Hammer presents Cameron as a man who very much believes, yet deludes himself, in sort of this honor that comes from his position that requires a certain attitude beyond even the mannerisms he has inherited along with his brother. Hammer shows Cameron as a man ready for every party, every general meeting or otherwise in the future in the way he speaks with such certainty towards his beliefs. Hammer grants this a touch of naivety even foolishness however not dishonestly through the character. There is some fun to be had at this expense, but this is part of the beauty of Hammer's performance. He allows you to have fun watching their plight, but he doesn't make them some sort of villain. They are still people.
On this point you can look at the way he depicts Cameron in two contrasting scenes. The first being one of his very best scenes where the two brothers go to lob a formal complaint about Zuckerberg to the president of Harvard. Hammer is downright hilarious in portraying Cameron's genuine disbelief at the president being completely unimpressed by his candor, and part of what makes this funny is how earnestly Hammer delivers every moment as a self-expressed "gentleman of Harvard". This can be contrasted against the series of court deposition scenes where we see a similair earnest disbelief in Hammer, however he garners a real sympathy when reacting to Zuckerberg's words of extreme disregard for the brothers. Now this is interesting as he iw distinguishing that against his portrayal of Tyler who has fewer pretensions over his position that Hammer realizes in subtle yet brilliant ways. Right in the disposition scenes for example it isn't the disbelief of a proper gentleman that he portrays rather fervent anger of someone ticked off who feels he was screwed out of a billion dollars. This idea Hammer directs throughout his work as Tyler that effectively differentiates between the two twins. In every moment of Cameron's assurance of proper manners of privilege, Hammer offers a terrific contrast through the more blunt of the two men who has no shame in using his wealth but also has no delusions around it either. One of my favorite deliveries of his in the film is "
I broke your 335-year old doorknob" after tearing off one of Harvard's valued furnishings, that perfectly exemplifies Tyler's attitude towards frankly sentiments of his own class. This is a great pair of performances by Armie Hammer as he excels as a combination of the two yet makes them distinct. He never falls to any pitfalls in playing twins and most importantly succeeds in crafting two entertaining characters yet still humanizes them perhaps beyond what is even their intended purpose within the story.