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But when the same Swedes were asked whether they would want to stay in the EU following a Brexit, 36% of voters said they would like to leave and just 32% said they would like to remain.
This poll is fascinating because Swedish voters are at odds with most Swedish politicians who are pro-EU. Swedes also have a track record of rebelling against their pro-EU political class. In 2003, they voted against adopting the Euro against the wishes of their Prime Minister Goeran Persson.
There are a few things at play here.
First off, Sweden and Britain belong to a minority of EU member states who don't use the Euro - if Britain leaves the EU, Sweden will suddenly find itself in a lonely position as the largest non-Eurozone EU member. Also, along with the Netherlands and Denmark, Britain is among Sweden's closest allies in the EU. The four countries have common interests and have worked together to try and reform the EU. If Britain leaves, it will become much less likely for reform to happen.
And perhaps most importantly, support for the EU has dropped since the start of the migrant crisis. Last year Sweden received 163,000 asylum seekers in 2015, more than any other country in the EU.
A Brexit really could be the start of something much bigger.