If you want to have input into the decision of a "private party" you can join the party.  The "open primaries" are what the people agreed to fund - and I agree if the public is paying for an election (primary) they have a right to dictate how it is held.  But candidate selection by a party is not really public business unless the party chooses to make it so - I do not think open primaries will serve the parties at all - each party should be able to select the candidate chosen by party members.  The real problem is in paying for the "election" - private party, private selection/election.  The public often forgets that political parties are private entities and do not have to abide by any rules set for them by outside parties unless they want the money associated with those rules to pay for conducting the primary.