Research has shown that the order of names on the ballot has a demonstrable effect on the outcome of the election. This implies that any fixed name order on the ballot gives some candidates an advantage over others. Tennessee law does specify a particular order for names to be on ballots, and I presume other jurisdictions do as well. It seems to me that such laws give some candidates advantage over others, and that only randomized ballots would thus be constitutional. Has this ever been addressed in court or by other legal authority?
Election Law is a power reserved to the states. As long as they comply with the 15th, 19th, 24th, 26th, amendments, it is constitutional. I would understand the argument that it violates the equal protection of the 14th amendment; however, if the practice is done uniformly and nondiscriminatory within the state, it should be fine. SCOTUS refused to hear a case involving the Nevada election ballot. The ballot contains an option for "None of the Above." In 1998, Harry Reid won re-election over then Republican Rep. John Ensign by 428 votes while more than 8,000 voters rejected both men and opted for "none." Clearly this unique ballot affected the race, and the nation (Reid is the Senate Majority Leader today).
EDIT: Pursuant to the comment below:
The 15th amendment says that the right to vote cannot be denied due to race. The 19th amendment gave woman the right to vote. The 24th amendment prohibits poll taxes. And the 26th amendment gives 18 years old the right to vote. Any election law must be compliant with these amendments.
As for the SCOTUS case: At the district court level, the court ruled the option to be unconstitutional; however, at the appeal level, the judge threw out the lawsuit and issued an emergency stay which allowed the option to stay on the ballot. I have not found any resource that explains the Supreme Courts decision not to hear the case.
Some background about the case: The Republican National Committee (RNC) challenged the law because if "None of these Candidates" received the majority of votes, it could not win the election and hold office. The Nevada Attorney General counter argued that the option was a form of protest and a offered the same outcome as someone who did not vote.