It turns out Elizabeth Olsen and I have something in common: when her call comes through from New York the morning after Barack Obama's stirring victory over Mitt Romney, we are both suffering post-election fog. The only difference is I've had too little sleep, and she's had too much.

Olsen, 23, was so tense ahead of the US's decision that she opted for the "wake me when it's over" technique. "I worked until eight o'clock, and I felt like a little kid staying up for Santa; I was nodding off on my couch waiting for Obama to make his speech. I tried so hard to stay awake!" she says, laughing at the memory. "I felt so ridiculous that I was a grown woman who could not stay awake for the election, but as soon as someone said, 'Looks like Obama has won', my whole body was like, 'You can sleep now.'"

It's a fittingly low-key introduction to the actress, whose brief but brilliant career has thus far been marked by fine work rather than tabloid-baiting frivolity, a surprise to those in the media who assumed the Olsen family – her sisters are actor-turned-designer twins Mary-Kate and Ashley, 26 – was little more than a celebrity-making machine. Her breakout performance as an escaped cult member in 2011's Martha Marcy May Marlene was one of the most impressive debuts in recent memory, praised by critic Roger Ebert as "childlike and yet deep, vulnerable but with a developing will, beautiful in a natural and unforced way".

Her latest role, in Josh Radnor's Liberal Arts (released here on December 13), couldn't be further from the paranoid and delusional Martha: she plays the bright and breezy Zibby, a 19-year-old college student who bewitches 35-year-old Jesse (played by How I Met Your Mother alumnus Radnor, who also wrote and directed the film) when he returns to his alma mater in the midst of a personal crisis. The part was something of a holiday for Olsen after a run of roles that left her emotionally exhausted.

"I really wanted to do something light-hearted because I'd done Martha, and [thrillers] Silent House and Red Lights, and it was all dark, dark, dark," she says. "I thought it was sweet, well-written and smart."

It's a testament to both Radnor's script and Olsen's performance that Zibby is not just another "manic pixie dream-girl" object of fantasy. Liberal Arts is as much a meditation on the very idea of higher education as it is a "romance". In an era where a degree no longer guarantees a career but still carries a hefty cost, Olsen, a student at New York University's Tisch School of the Arts, is aware of the privilege inherent in being able to study.

"When you're a teenager, you become aware that there are things that cost a lot in the world, and one of them is education," she says. "For me, I became really obsessive about being appreciative of it. That meant appreciating my teachers more, which made me want to work harder in school, because I didn't want them to feel like what they were doing was for nought; I wanted them to know that I respected them, and that I cared."

The notion of "learning for learning's sake" (something a liberal-arts degree typifies) is also something that appeals to Olsen, who was thrilled to find her coursework involved academic electives in addition to acting.

"When I went to college, to study theatre, for every academic class I had to take, I just wanted to take anything that was of interest to me in general, because I believe that it's worth it to be knowledgeable about things that have nothing to do with your job; I think it makes you a more rounded person," she says. "And so, it doesn't make any sense if you look at my academic record, but to me, every class meant something. I think it's important, especially if you work in the arts, because you're in this isolated environment; art doesn't create art, life creates art."

It's a marked difference in attitude to those of her peers who are concerned only with immersing themselves in the role they are working on. She laughs uproariously at the image of an aspiring actor locked in a rehearsal room, obsessively concerned with their character's "motivation".

Unlike her sisters, whose acting careers began at the age of nine months when they were cast in the shared role of Michelle Tanner on Full House, Olsen emerged in Martha Marcy May Marlene seemingly fully formed. She didn't toil in obscurity or pay her dues on the "child actor" circuit, though not for lack of trying. "I've never been on Law & Order – I've auditioned for it! – but I never got those jobs," she says.

Instead, Martha, the first film to be released of four she worked on in a short time frame, provided her with a storied entrance into the industry. "I'm really lucky to have had the first film of mine that was released put me in a position where jobs, all of a sudden, aren't too much of a struggle to try and get; that's so rare and exciting. The films I'm doing or are going to be doing were chosen for very specific reasons – not just for 'work', but to grow from and learn from. It's a playground right now."

A professional playground, perhaps, but one tempered, in some quarters, by media whispers about how much clout the Olsen name carries. Or, as such speculation puts it more bluntly, did Olsen get a piggyback into the industry simply because she's "Mary-Kate and Ashley's sister"?

"I think everyone has a set of challenges that they have to overcome, and mine just happened to be a little different, because it had to do with things like public perception," she says. "You know, if you're going to be a lawyer and your dad owns a firm, that can actually be a great help, but everyone thinks it's nepotism; you have to make sure that you know it's [because of] you, and people can say what they want."

And "people" certainly do. Indeed, it's surprising that her sisters' treatment at the hands of the often merciless celebrity-gossip media – particularly Mary-Kate, whose romances and 2004 treatment for anorexia nervosa have been well documented – wasn't sufficient deterrent to send her into small-town chartered accountancy rather than acting.

"My sisters happen to be people who don't ask for it, they just happen to be people who get it," Olsen says of paparazzi attention. "They don't go to events or go to restaurants that people are waiting out front of with cameras, they don't put themselves out there to be photographed."

It seems the idea of "celebrity" holds little appeal for Olsen. And though it might be tempting to dismiss her approach to Hollywood - "you just try to find a balance" - as springing from the same sort of youthful idealism as that espoused by Liberal Arts's Zibby, Olsen is far more grounded. "I never understood why someone would seek fame out, because I find it to be scary, that lack of privacy. But I don't really foresee having those issues. I don't know why, I just don't think I will. A lot of young actors I've worked with have the same mentality, there's no goal of superstardom, they just like to work a lot."

And work is what Olsen plans to dedicate herself to, more or less. "My ideal is to maintain a balance between projects that have a larger importance to me, and ones that just seem like a good time," she says. "The truth is, acting becomes this livelihood where you leave your real world for a couple of months and you create this new family, and if that new family is really dysfunctional and makes you feel angry every day, it's really not worth it. It might be a huge, career-defining whatever, but if you know that you're going to be miserable, I don't think that's worth it. I have a lot of drive, and I'm a workaholic, but I really think quality of life is important."

And if that means sleeping through President Obama’s acceptance speech, so be it.

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