Who said 1-2-3 was easy?

After two years of struggle, and a lawsuit filed on behalf of voters, the Department of Elections on Thursday unveiled its new ballot, which will allow voters to support up to three candidates in The City's first experiment with instant-runoff voting.

The new 1-2-3 ballot, unveiled at City Hall, lists the entire field of candidates three times, allowing voters to back other candidates as alternatives in what's known as instant-runoff voting or ranked-choice voting.

The system allows voters to rank each candidate so that if their first choice was the lowest vote-getter, their vote would then go to their second choice, and if that candidate was eliminated, the vote would go to the third choice. Candidates are eliminated by receiving the lowest amount of votes.

Advocates, such as Supervisor Matt Gonzalez, pointed out its main benefit: "You can have a majority winner with one trip to the ballot box," avoiding the run-off elections that have plagued The City in mayoral and supervisorial elections, he said.

Gonzalez added that ranked-choice voting allows people to cast their first ballot for whichever candidate they truly would like to see in office without harming another acceptable contender who may have a better chance to win.

San Franciscans passed Proposition A two years ago as a way to save millions by avoiding follow-up elections between the two top vote-getters in races for supervisor, mayor and five other elected offices. But then came months of struggles to implement it, since no existing computer system filled the bill and critics threatened to sue.

The measure's timeline called for a first test in last year's mayoral race, but elections officials said they were not ready. After a lawsuit was filed to force their hand, a judge chided The City for failure to enact the will of the voters.

Political Science Professor Rich DeLeon, of San Francisco State University, said ranked-choice voting isn't new. Versions of it have been used in cities such as Cleveland, Toledo, Cincinnati and Cambridge, as well as abroad.

He calls it a "natural experiment" that has already led to a more harmonious campaign in The City's seven districts where supervisors are being chosen this year.

"By now there would usually be a few gallons of blood on the floor," DeLeon said.

Elections chief John Arntz is spending a total of $776,000 on a citywide mailing to help educate the public with brochures in English, Spanish and Chinese, and an interactive Web site where people can try out the IRV method. He has set up a team of at least nine community groups to target voters who may be confused by the new system, particularly in minority and low-income areas. Speakers will also be available to make presentations to community groups that would like to learn about the new ballot. The information number is (415) 554-4375.