Indiana currently does not have registration by party. On primary day, voters ask for any particular party’s primary ballot. Representative Dan Stevenson (D-Highland) has introduced HB 1404. It would provide that a primary voter decides in the secrecy of the voting booth which party’s primary to vote in. As before, though, a voter could only vote in one party’s primary.
There’s also a movement in Illinois to change from “open primary, public record” to “open primary, private choice” (the proponents of the change refer to the two systems as the “closed primary” and the “open primary”).
In 2006, nonbinding votes were taken in a number of Illinois municipalities, and “open primary, private choice” won all of them by substantial margins.