Final answer:
An open primary allows voters to choose which party's primary to participate in on Election Day without revealing their party membership, unlike closed or semi-open primaries.
Step-by-step explanation:
The type of primary being described where voters need not reveal their party membership and can choose the ballot of the party's primary in which they would like to vote, where all voters and independents have freedom of choice, is known as an open primary. In an open primary, voters are not required to be members of a specific political party to vote in that party's primary election. This system is contrasted with the closed primary, where only registered members of a party can vote in that party's primary, and the semi-open primary, where individuals declare their party ballot choice on Election Day but must stick to one party's primary. The purpose of an open primary is to allow for greater voter freedom and participation, although it does raise concerns about 'raiding,' where members of one party might vote in another party's primary to influence the selection of weaker opponents for the general election.