"Possibility" was well received by music critics. Todd Martens wrote for the
Los Angeles Times that Li "could melt the coldest of hearts with this sparse tearjerker. A slight scratch in her vocals cuts through the song's intimately innocent feel. 'Tell me when you hear my heart stop,' she sings, while a backing choir inflects the sparse piano with
gospel undertones—a brief, largely
a cappella prayer."
Dose magazine referred to the song as "one of the more gripping mope-outs on the disc. The Swedish pop-singer coos in a cracked-with-emotion whisper, accompanied by a barely-there piano, as she pines for a lover."
Consequence of Sound critic Anthony Balderrama noted that Li "channels some of the more intimate moments of her short career on 'Possibility'. It evokes the vulnerability she's so good at cooing, just as she did in the simple 'Time Flies' and 'Tonight' off of [her album]
Youth Novels. At five minutes, the locomotive rhythm and clunky piano borders on plodding, but the overall effect is so depressing that it works better than it should."
IndieLondon rated the song four out of five, stating it is "as beautiful and haunting as we've come to expect from this Swedish performer... and perfectly ethereal to accompany staring out the window at a snowy landscape. If it wasn't essential beforehand, it damn sure is now!" Marc Hogan of
Pitchfork commented that the "feedback-streaked piano ballad 'Possibility' is a relative bright spot, but like the rest of the tracks [on the soundtrack], it pales in comparison to the work on her own records." Krista Richmond of
KillerFilm called the song "lovely in its haunted, enchanting way" and added that it is "soft and melodic enough to pull at even the toughest of heartstrings".
MusicRadar's Joe Bosso opined that "[t]his stark, piano-based
hymn is spiritual stuff, and Li's arresting vocal powers will have you on your knees in worship." Adam Pfleider of
AbsolutePunk expressed that "Lykke Li is where the problem of the soundtrack lies. I can't listen to this music without thinking of where it will end up in the
melodrama of some teenager metamorphosing into a
CGI werewolf. 'Possibility' is a beautiful song, but I can't help feeling its placement in the film would kill its blossoming melody in the end." In December 2009, the song was announced as one of the sixty-three songs to be shortlisted for the
Best Original Song category at the
82nd Academy Awards, but did not make it to the final list. ==Music video==