The numbers are attention-getting: on Tuesday, New York City will spend about $13 million to hold a runoff in the Democratic primary for an office, public advocate, that is budgeted only $2.3 million a year. And the combination of a little-known post with a little-understood election process is expected to lead to startlingly low turnout — maybe 100,000 to 175,000 voters, in a city of 8 million people. Yet the election is likely to determine the occupant of one of the city’s top offices, because there is no Republican candidate.

The high cost of an election for a low-cost office has inspired wags to muse. Some have suggested that the race be decided by a coin toss. Others, including the Republican nominee for mayor, Joseph J. Lhota, have joked that, because the public advocate has few concrete powers, the two candidates could be allowed to serve, at a saving to taxpayers.

But some elected officials and government reform advocates have suggested a longer-term solution: instead of holding costly, low-turnout runoffs, New York City should switch to instant runoff voting, a system already used in other cities.

In cities with instant runoffs, voters rank candidates by order of preference. If no candidate surpasses the minimum threshold to win an election, the last-place finisher is eliminated, and those votes are redistributed according to the preferences on the ballots. The process continues until a candidate crosses the threshold.