The anti-establishment party founded by hackers and activists look set to either win or come in a close second in Iceland's parliamentary elections.

Formed four years ago by a group of anarchists and internet freedom activists, the Pirate Party caught the attention of the media by stating they wanted to decriminalise drugs. They are also keen to offer whistleblower Edward Snowden political asylum.

Its policies include a right to privacy and a right to anonymity, a call for government data to be open and in open data formats. The party is also formulating a plan to to make Iceland a data haven in which information cannot be disclosed, an arrangement akin to Switzerland's role as a haven for secret financial dealings, according to The Register.

After the Charlie Hebdo shooting in January 2015, the Pirate Party launched a campaign to successfully repeal Iceland's blasphemy laws. The repeal read: "Freedom of expression is one of the cornerstones of democracy. It is fundamental to a free society that people should be able to express themselves without fear of punishment, whether from the authorities or from other people."

During the vote, the three Pirate Party members stood up in the Icelandic parliament and shouted in solidarity: "Je suis Charlie".

In 2013, the party took 5% of the vote, winning three seats in the 63-member parliament in Iceland. Analysts are predicting that the Pirate Party could take up to 20 seats, putting them in a strong position to form a government in a coalition with other parties. This is purely theoretical because the radical party has already ruled out forming a coalition with the two ruling parties – the Independence party or the Progressive party.

Today, a recent poll by local newspaper Morgunblaðið and the Icelandic Social Science Research Institute of the University of Iceland reports that support for the Pirate Party is running at about 22.6%, a point-and-a-half ahead of the ruling Independence Party and four points clear of the Left-Greens.

However, Birgitta Jónsdóttir, the party leader, claims she has no intention of being prime minister, according to a Guardian report.

The 49-year-old feminist, poet and former WikiLeaks collaborator wants to see a different kind of political system, as in the Pirate party's horizontal structure. "We do not define ourselves as left or right but rather as a party that focuses on the systems. In other words, we consider ourselves hackers – so to speak – of our current outdated systems of government."

Parliamentary candidate Smári McCarthy explained. "Despite our name, we're taken fairly seriously in Iceland, in particular because of our very aggressive anti-corruption stance, [and] our pro-transparency work."

The radical group are particularly popular with the young. "All the old parties have been tried out, you can say that, since the (financial) crisis, and people have not been happy with how they managed austerity or how they managed the economy, and people have also been calling for more democratic reform, and this kind of opens up a space for new parties," said Eva Heida Onnudottir, a politics professor at the University of Iceland in a euronews report.

Polling stations across the island opened at 07:00 GMT on Saturday (29 October) and are due to close at 20:00 GMT, with first results expected soon afterwards at around 10 pm (GMT) when polls close. The final outcome may not be clear until the last vote has been counted on Sunday morning.