PHOENIX — Democrats allege the design of Arizona ballots puts their candidates at an unconstitutional disadvantage, according to a lawsuit filed last month against Arizona’s Secretary of State.

The suit takes issue with ballots in partisan races that routinely list Republican candidates before Democrats, and it recommends rotating ballot order to ensure no candidate has an advantage.

Arizona law dictates that each county’s ballot order be determined according to the votes cast for governor in that county in the most recent general election. Candidates from the party of the gubernatorial candidate with the most votes are listed first, followed by candidates from other parties. This applies to all partisan races, including for president, Congress and many state races.

Under the law, the ballot typically is led by a party that has been dominant in recent years in Arizona, said Dave Wells, a political science professor at Arizona State University.

“Republicans typically win most of the counties,” Mr. Wells said. “That would mean that Republican candidates get privilege.”

According to the lawsuit, filed Nov. 1 in U.S. District Court in Phoenix, Republican candidates will be listed before Democrats in 11 of 15 Arizona counties in the 2020 general election. This includes Maricopa County, where Gov. Doug Ducey outpolled his Democratic rival, David Garcia, by more than 200,000 votes in 2018.

Wells said ballot order may affect third-party voters even more than Democrats.

“Independent voters would be the most strongly impacted by the ballot order,” he said. “They (voters) look at it, and they’re going to see whoever’s first on the ballot. And that’s just the way our brain works.”

The lawsuit — filed by the Democratic Senatorial Campaign Committee, Democratic National Committee, Priorities USA in Arizona and two Arizona residents — claims a political phenomenon called “position bias” affords electoral benefits to candidates listed first. Similar suits were filed in Georgia, Texas and Minnesota.

The Democratic groups hope courts find Arizona’s ballot order statute unconstitutional. The plaintiffs recommend alternating the order of candidate names based on precinct, ensuring each candidate is listed first on a proportional number of ballots. Arizona randomizes ballot order in primary elections to avoid preferential placement, but general elections are not randomized.

The lawsuit points out that ballot order is especially important in the 2020 general elections, where “Arizona is projected to have numerous highly competitive races,” including Mark Kelly’s bid to oust Sen. Martha McSally, R-Ariz.

Democratic lawsuits also target Texas and Georgia — also considered battleground states next November. And Minnesota voters filed suit Nov. 27 alongside the Democratic Senatorial and Congressional Campaign committees, claiming unfair bias in ballot order.

On Nov. 15, Florida Democrats won their ballot order lawsuit, and a court overturned the state’s law allowing the party that holds the governor’s office to list its candidates first on general election ballots. The lawsuit claimed this law favored the Republican Party, which has held Florida’s governorship since 1999.

Sen. Catherine Cortez Masto, D-Nev., the chairwoman of the Democratic Senatorial Campaign Committee, said the victory in Florida will help states facing similar ballot problems.

“No candidate or party should benefit from an unfair advantage in our elections, and we will take every step available to correct these unconstitutional mandates,” she said. “Voters should have faith that elections are fairly administered without bias, and that applies to the ballots they cast.”

The Republican Party of Arizona issued a statement via communications director Zach Henry, dismissing the lawsuit.

“Rather than working to ratify the USMCA or lower prescription drug costs, Democrats are preoccupied with political trivia,” Mr.Henry said, referring to the United States-Mexico-Canada Agreement on trade. “The order on the ballot isn’t the Democrats’ problem — it’s how out of touch they are with the issues Arizonans care about.”

Maricopa County Recorder Adrian Fontes said his office hasn’t seen significant evidence of a problem with the ballot order.

“Specifically, as to which candidates get listed first, we rarely hear any of those complaints,” Mr. Fontes said. “But we’re always looking at ballot design improvements.”

Regardless of the lawsuit’s outcome, Arizona general election ballots are getting updated.

“The most notable change in the new ballot design is going to be the absence of the arrows,” Mr. Fontes said. “They’ll be replaced by ovals where you fill in your choices.”