Well it would be an interesting one. Normally a very low turnout wouldn't deter the politicians from pressing on regardless, but in this instance, with EVERYBODY in the country declining to endorse any politicians, government in the traditional sense would be unviable. The queen could simply appoint a government, but that would be overturning the wishes of every single one of her subjects - and she couldn't even rely on the army to quell dissent since they would be 100% non-voters as well.