(a) The Legislature shall provide for primary elections for partisan offices, including an open presidential primary whereby the candidates on the ballot are those found by the Secretary of State to be recognized candidates throughout the nation or throughout California for the office of President of the United States, and those whose names are placed on the ballot by petition, but excluding any candidate who has withdrawn by filing an affidavit of noncandidacy.

  (b) A political party that participated in a primary election for a partisan office has the right to participate in the general election for that office and shall not be denied the ability to place on the general election ballot the candidate who received, at the primary election, the highest vote among that party's candidates.