As provided in this article, a presidential preference primary shall be held in 1992 and every four years thereafter for each political party or body which has cast for its candidates for President and Vice President in the last presidential election more than 20 percent of the total vote cast for President and Vice President in the state, so that the electors may express their preference for one person to be the candidate for nomination by such person's party or body for the office of President of the United States; provided, however, that no elector shall vote in the primary of more than one political party or body in the same presidential preference primary. Such primary shall be held on March 3, 1992, and on the first Tuesday in March every four years thereafter. A state political party or body may by rule choose to elect any portion of its delegates to that party's or body's presidential nominating convention in the primary; and, if a state political party or body chooses to elect any portion of its delegates, such state political party or body shall establish the qualifying period for those candidates for delegate and delegate alternate positions which are to be elected in the primary and for any party officials to be elected in the primary and shall also establish the date on which state and county party executive committees shall certify to the Secretary of State or the superintendent, as the case may be, the names of any such candidates who are to be elected in the primary; provided, however, that such dates shall not be later than December 31 in the year preceding the year in which the presidential preference primary is to be held.