What if you gave an election and no one showed up? I’m talking to you, Los Angeles.

Last Tuesday, about 16 percent of the registered voters showed up to pick the mayor of the country’s second-largest city. But don’t worry, when all the ballots are tallied the final figure could rise as high as say, oh, 19 or 20 percent.

When the leading candidate for mayor, Eric Garcetti, collects the votes of fewer than 100,000 of the city’s 1.8 million registered voters, it’s not time for fiddling around the edges of voting rules. Go big or go home.

If Los Angeles really wants a truly representative election, the city needs to go 100 percent vote-by-mail. Right now.

It’s not that shocking an idea, really. More than half of California’s votes were cast by mail last November. For the lower turnout June primary, it was 65 percent.

Even in Los Angeles, which for a variety of historical reasons has one of the lowest percentages of permanent vote-by-mail voters in the state, more than 40 percent of those voting in last week’s election cast ballots by mail.

People like to vote by mail. It’s fast, it’s convenient and that ballot on the table in the hallway is a constant reminder that an election is coming and that your polling place is your mailbox.

In California, the number of mail ballots cast is growing in each election. In Oregon and Washington, all their elections are mail-only.

How’s that working out? In November, the statewide turnout was 81.2 percent in Washington and 82.8 percent in Oregon.

Sure, Los Angeles has a population of 3.8 million people and city election officials have argued for years that makes it both too complicated and too expensive to encourage the increased use of mail ballots. But somehow the state of Washington, population 6.8 million, manages.

Right now only a couple of the state’s smallest rural counties use all-mail elections. But most counties in California have used all-mail votes for small-scale elections of various types. And even San Mateo County, no population Goliath, has some 90 precincts, mostly small and isolated, where all voters must cast ballots by mail.

Heck, in 2007, the Los Angeles City Council asked for a staff study on moving to all-mail elections. That study found that the change would both save money and boost turnout.

The message wasn’t entirely cheery, however. “Administering such elections raises some administrative challenges,” the report found.

But any difficulties pale next to the unsolvable political problem of trying to govern a huge, diverse city with the support of only a relative handful of voters.

For years, California counties looking at ways to cut their election budgets have been arguing that the state needs a full-scale test of mail-only elections. You can’t ask for a better testing ground than Los Angeles.

And for Los Angeles and its 16 percent turnout, something drastic needs to be done to bring people into the political process. And quickly.

John Wildermuth is a longtime writer on California politics.