How to improve Primary Election Turnout: Let Everyone Vote

My state had a primary election this week and once again the press and election officials bemoaned the fact that turnout was light. They blamed it mostly on electoral apathy. I submit that a more direct cause is the fact that only registered party members can vote in a primary. That means that one third or more of the electorate, including myself, who are registered independent or unaffiliated cannot vote. Now coupled with the apathy factor you get a turnout of between 15% and 25%.

I suggest doing away with preregistration of party affiliation. You would still register to vote, but you would not indicate a party. Then, when you arrived at the polling station during a primary election you would tell the poll worker in which party's primary you would be voting and would be instantly registered with that party. You would remain registered with that party until you voted in another primary. Only registered voters who never voted in a primary would remain unaffiliated.

This would allow all voters to participate and improve voter turnout. There are a number of primaries in which I wished I could vote, but can't because I am registered independent. Of course I could reregister as a party member, but that is a hassle if I want to change my affiliation from one election to the next. Anything that improves voter turnout should be encouraged.