This has become the first major American city to adopt an instant runoff system for nearly all municipal races, allowing voters to rank candidates as their first, second and third choice.

The preferences would be used to pick a winner if no candidate for a city office got more than 50 percent of the vote. That would eliminate the need for voters to return to the polls weeks later to choose between the top two vote-getters who have advanced to the runoff.

The instant runoff was approved by 56 percent of city voters in a March 5 referendum. It is not certain that the system will be in place by the November elections, officials said, because new computer software must be installed.

Opponents have criticized instant runoffs as undemocratic and confusing. Proponents have said it will open the political process to more outsiders and save money, because runoffs cost taxpayers about $1.6 million each.

"It will benefit the city in terms of the millions of dollars it will save and also the wear and tear on the Department of Elections," said Mark Leno, a member of the city Board of Supervisors. "It will encourage greater voter participation."

Turnout in runoffs in San Francisco has been distressingly low, some officials say, because those races are held shortly before Christmas.

Chris Bowman, a Republican political consultant and former member of the San Francisco citizens advisory committee on elections, said the instant runoff violated the one-person-one-vote principle.

The concept has been used for decades in Australia and Ireland. London recently elected its mayor using the system, and Cambridge, Mass., has been electing City Council members through instant runoffs since 1941. Alaska will have an instant- runoff referendum on the ballot this fall.

The San Francisco system will differ from the one in Cambridge, where voters pick from a slate of candidates to fill multiple slots, a method that makes it possible to win with only 10 percent of the vote.

In San Francisco, the process will be used for most major city offices, including mayor, treasurer, district attorney, public defender and members of the Board of Supervisors.

Under the system, the candidate with the fewest votes is eliminated, and the second choices of voters who selected that candidate are added to the tallies of the remaining candidates. If this does not create a winner, the process is repeated until someone gets a majority. (If a voter's first and second choices are eliminated, his third choice is applied to the remaining candidates.)

Among the most prominent supporters of the referendum were minor parties, particularly the Green Party, which say the instant runoff could benefit them because voters could choose both their candidate and a major-party candidate.