On November 1, the Democratic Party sued Arizona over the law that controls the order of names on the ballot for partisan office. The Arizona law says the top names on the ballot are the nominees of the party that got the most votes in that county for Governor in the last election. Republicans have the top line in all but four counties. Here is the Complaint.
The case is Mecinas v Hobbs, 2:19cv-5547. It is assigned to U.S. District Court Judge Diane Humetewa, an Obama appointee. The Complaint says in a footnote that if the Democrats win the case, it does not follow logically that the relief should extend to any minor parties. The justification for that conclusion is that the U.S. Supreme Court said in Timmons v Twin Cities Area New Party that states have an interest in promoting the two-party system. That conclusion, written by Chief Justice William Rehnquist, was supported by no evidence and no argument by either side in the case. Rehnquist did not define “two-party system”.