ST. PAUL — Voters in Minneapolis today confronted a ballot containing 35 candidates for mayor and a potentially confusing process of choosing first, second and third choices in the race.

The decision by Mayor R.T. Rybak not to seek a third term, paired with the city’s unusually low $20 filing fee, prompted the flood of wannabe successors. And the system known as “ranked choice voting” — in place since 2007 but getting its first real test this year — eliminated the traditional primary election that would have winnowed the field.

In this off-year election, residents in a number of Minnesota cities are choosing mayors and council members. Minneapolis and St. Paul both have mayor’s races, but in the capital city, incumbent Chris Coleman was heavily favored to win a third term.

In addition, 76 school districts were asking for some kind of financial help from voters through either operating, building or capital project levies.

But the most-watched has been the muddled mayor’s race in Minneapolis. The low filing fee gave a host of oddball candidates a spot on the lengthy ballot: from an Occupy Wall Street activist named Captain Jack Sparrow, to frequent candidates Bob Carney and Ole Savior, to representatives of such unique political parties as Legacy-Next Generation, Local Energy/Food, and Pirate Party (oddly enough, not Captain Jack Sparrow).

Eight of the 35 candidates have run more traditional and well-funded campaigns. But Democratic activists in this heavily liberal city left the race without a clear front-runner when they deadlocked last summer over whether to confer the party’s endorsement on Betsy Hodges, a city councilwoman, or Mark Andrew, a former Hennepin County commissioner.

And Rybak, who last won re-election with nearly 73 percent of the vote, declined to endorse a successor.

Besides Hodges and Andrew, other leading candidates have been Don Samuels, a city councilman; Jackie Cherryhomes and Dan Cohen, both past council presidents; Bob Fine, a member of the local park board; Stephanie Woodruff, a businesswoman; and Cam Winton, an attorney and moderate Republican.

Minneapolis residents approved ranked choice voting in a 2006 referendum. It was sold as a progressive reform that eliminates the cost and burden of primary elections, and theoretically gives voters more say through the ranking system.

Under that system, if no candidate exceeds 50 percent of first-choice votes, that triggers a series of automatic runoffs in which lower-ranked candidates are eliminated and second and third choices are redistributed to remaining candidates’ totals.

“I don’t really understand it,” Alyson Frahm, an art director at Target who lives in the city’s Bryn Mawr neighborhood, said of ranked choice. Asked her top three choices not long before Election Day, Frahm said she was still undecided: “Mainly, I’m disappointed Rybak isn’t running again.”