Professor Daniel Ho, an expert in quantitative empirical legal studies and election law, is quoted in this article about ballot position's effect on votes:

Independent gubernatorial candidate Chris Daggett plans to file a lawsuit arguing that New Jersey's balloting system is unconstitutional because it gives the two major parties top billing, his spokesman said yesterday.

New Jersey gives the prime ballot spots in the general election to the Republican and Democratic candidates, while the remaining candidates fill out the rest of the spots.

...

"For general elections, there's much less evidence for a wide effect on major party candidates," said Daniel Ho, an associate professor at the Stanford University law school. "There's some evidence that it affects minor party candidates."

The impact on elections, however, is small, he said.