The Minnesota Democratic-Farmer-Labor Party filed a lawsuit last year against the state’s law on ballot order of candidates on the general election ballot for partisan races. The law says the top line should be for the nominees of the ballot-qualified party with the smallest amount of support (as measured in the previous general election). The next line is for the second-weakest ballot-qualified party, etc. Because Minnesota had only the Republican and Democratic-Farmer-Labor Parties as qualified parties before 2018, that meant that for 2018, the Republican Party had the top line, followed by the Democratic-Farmer-Labor Party.
In November 2018, however, two more parties became ballot-qualified: (1) Legal Marijuana Now; (2) Grassroots-Legalize Cannabis. This meant that for 2020, the nominees of those two new parties would be on the top two lines, Republicans would be next, and finally Democrats. Underneath them would be the nominees of the unqualified parties and the independent candidates, in order of filing their petitions.
The Democratic Party lawsuit is still pending. On May 11, both sides submitted a joint statement regarding potential relief. The Democratic Party now favors rotating the names of all candidates (even the nominees of unqualified parties) within each precinct, so each candidate would have an equal chance to be listed first within each precinct. The state prefers a lottery, in which the four qualified parties would participate to determine the order for them only, for the entire state. Here is the Joint statement. Pavek v Simon, 0:19cv-2995. U.S. District Court Judge Susan R. Nelson will now presumably pick one of these two choices.