Basically, in 2009 he formed the "Best Party" with a number of other people with no background in politics. A satirical political party that "parodies Icelandic politics and aims to make the life of the citizens more fun," somehow managed a plurality win the 2010 municipal elections in Reykjavík, with the party gaining six out of 15 seats on the Reykjavík City Council (34.7 percent of the vote). Gnarr became mayor, which was widely seen as a backlash against establishment politicians in the wake of Iceland's sill ongoing financial crisis.
Jón's political platform included -- seriously -- "free towels in all swimming pools, a polar bear for the Reykjavík zoo, all kinds of things for weaklings, Disneyland in the Vatnsmýri area, a 'drug-free' Althing by 2020, sustainable transparency, tollbooths on the border with Seltjarnarnes, to do away with all debt, free access to Hljómskálagarðurinn (orchestral rotunda park)."
Even better, when he was elected he announced that he would not enter a coalition government with anyone that had not watched the "The Wire."
I had the genuine honor of his handshake before watching him hilariously introduce Dario Argento, who also seemed to find Gnarr hilarious. Here's a video of the fete, followed by Argento accepting his award:
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