The best way to explain the party declaration on the outside of the ballot is that it is a sorting issue and not actually a party declaration. You have to realize that the presidential primary is a function of each separate party. So, you are essentially marking on the outside envelope which party's primary you intend to vote in. So, there are actually two elections on this ballot, and you only have the choice to vote in one. The mark on the outside of the envelope then tells the election workers, who are sorting the ballots, which primary you voted in. I'm not saying I like it, but it is a matter of convenience and efficiency for election workers who are also tasked with counting your votes as quickly as possible. In the end, anyone can choose to vote in whichever primary they want, or none at all. All you are doing is choosing that party's nominee.
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