TALLAHASSEE — Rick Scott won two close races for governor by a single percentage point. President Donald Trump carried Florida by 1.2 points in 2016.

The two Republicans ran in different years, but they had something in common. Their names appeared first on the ballots, above those of their Democratic rivals, and Democrats argue in a lawsuit that Republicans no longer should enjoy an unfair advantage.

In Florida, the listing of candidates in partisan races favors the party that controls the governor's office. Some states such as Ohio, New Hampshire and Montana rotate names of candidates between counties or precincts.

Now, with Democratic Sen. Bill Nelson in the fight of his political life, and with polls showing a very close race, Democrats want to change the ballot order law that they say creates "position bias," calling it "an invisible thumb … on the scale in favor of Republican candidates."

The Democratic National Committee, its three congressional and legislative campaign groups and a progressive advocacy group, Priorities USA, want a federal judge to strike down Florida's 67-year-old law, which for most of that time favored Democrats, and replace it with a random system.

The case is assigned to U.S. District Judge Mark Walker in Tallahassee — the same judge who in February ruled that Florida's system of restoring voting rights to people with felony convictions is unconstitutional. The state has appealed the decision and a federal appeals court will hear arguments in Atlanta on Wednesday.

READ MORE: Judge strikes down Florida system for restoring felons' rights

Democrats want the ballot order law changed before the November general election, and the first ballots must be shipped overseas by Sept. 22.

The first race listed on every November ballot will be the marquee Senate match-up between Scott (listed first) and Nelson (listed second).

Democrats hired a Stanford University political scientist, Dr. Jon Krosnick, who cited a series of studies showing that a candidate listed first is worth 2.7 percentage points for Republicans and 1.96 points for Democrats. The same preferences appear in studies of consumer tastes and students who take multiple-choice tests, Krosnick's report said.

Not mentioned by Democrats is the fact that Nelson won three U.S. Senate races in a row, despite being listed second on the ballot in 2000, 2006 and 2012.

But Democrats have lost 21 of the past 25 statewide partisan races in Florida (the only other Democratic winner was CFO Alex Sink in 2006).

Scott's administration defends the current law, noting that it was created by Democrats in 1951, and that changing the ballot style now would be costly to taxpayers and confusing to voters.

"Granting the injunction will also hinder the smooth administration of elections," the state argues. "This is especially true given the number of ballot styles election administrators will be required to proofread and print, increasing the likelihood of error."

The state has the support of the Republican Governors Association and the National Republican Senatorial Committee, groups that support Scott's Senate campaign.

To bolster their case, Republicans cite an affidavit from Okaloosa County Supervisor of Elections Paul Lux, who chairs a statewide association of county election officials.

Citing his 20 years of election experience, Lux said changing the ballot order law now "could lead to catastrophic failures," far worse than a 2012 equipment malfunction in Palm Beach County that resulted in misreporting some results.

Like most county supervisors, Lux said he publishes a sample ballot in local newspapers before Election Day. If a court orders a rotational ballot system, the published sample ballot may differ from the ones voters see when they vote, he said.

A former supervisor of elections, Tallahassee's Ion Sancho, disagreed and said changing how candidates are listed "would not constitute any added administrative burden" for counties.

Scott won re-election as governor four years ago over Democrat Charlie Crist by a margin of 64,145 votes out of nearly 6 million cast.

Democrats initially asked that candidates' names rotate between precincts, but they changed their proposal to a county-by-county rotation, which the Scott administration calls a "bait and switch" tactic.

The two sides will square off in a Tallahassee courtroom on Tuesday and Scott's side has called as a witness Miami-Dade Supervisor of Elections Christina White, who already must print ballots in three languages — English, Spanish and Creole — and who has nearly 900 precincts.