In the final days ahead of the vote, Iceland’s prime minister, Kristrún Frostadóttir, has sought to remind voters that the referendum is not the end of the matter, and that there will be another referendum if and when a membership agreement with the EU has been reached.

“This is not an election about membership and not about adaptation, as there will be another referendum on an accession agreement if the result is yes,” Frostadóttir told a rally.

Fish is not just an economic matter, it’s part of the national identity 

For many, Iceland’s national identity and ultimately its culture is on the ballot too.

Iceland, which gained independence from Denmark in 1944, has a proud history of independence, of not allowing itself to be pushed around by bigger and richer European nations. It even fought – and won – the so-called Cod Wars with Britain in the 1970s over its fishing grounds.

Backers of EU membership say it’s best for Iceland to get closer to its European neighbours to combat issues that don’t respect borders, such as climate change.

Iceland is already in the EU’s frictionless single market and the Schengen free-travel zone.

Opponents say the current setup is just right and that Iceland already enjoys all the benefits of European integration without the sovereignty compromises that inevitably will come from being a full member.

“I think Iceland is better off outside of the EU, within the close collaboration with the EU,” former Prime Minister Katrín Jakobsdóttir told The Associated Press.