In less than 15 weeks, Washington will have picked its mayor for another four years -- and the big money is on the man who's got the job already. It's lots of big money, and it's saying that Marion Barry -- in spite of all the troubles that have surrounded him -- looks far stronger than anybody else in the running or still toying with the idea. Why no big challenge?

Barry may not be universally loved, but he is politically courted. While New York City Mayor Ed Koch may run around the Big Apple asking, "How'm I doing?" -- and hearing "worse and worse" these days -- Barry doesn't ask. He tells you. "I'm looking for competition. I welcome it." And as galling as his conceit can be to those who would prefer either more humility or somebody else in the city's highest office, he has some cause for his confidence:

*By big-city standards, the local government here -- arguably the second most complex in America behind New York's -- has been functioning reasonably well.

*By serious campaign standards, there seems to be no candidate willing, financed, prepared or popular enough to mount an effective challenge between now and the Sept. 9 Democratic primary -- which, barring a general election miracle, is when Washington will make its choice.

But how does Barry wind up sitting so pretty? Is it luck, skill or the spoils of an embryonic political world in the District of Columbia?

There's been corruption -- enough to send Barry's top deputy to prison; and other top aides have left with something less than high honors, while federal prosecutors and grand juries continue to investigate. You would think this might stir some major-league local figure into the mayor's race, but no -- the candidate doing the most talking about the Ivanhoe Donaldson case and other issues of "public trust" is Barry, in a preemptive blitz of meetings around the neighborhoods in which he makes much of the fact that "99.9 percent of our public employees are honest."

In the absence of a well-known opponent, Barry has been able to systematically woo the support and dollars of significant political blocs across the city, including business leaders, labor groups, bankers, gay organizations, many of the elderly, the arts and humanities crowd and women's organizations.

Still, there's plenty that hasn't been working well: housing, which the federal government has had to step in and supervise; the overcrowded jail and prison system; the disorganized assistance to the homeless; and the annual bumper crop of crater-sized potholes.

So where is the opposition? People look first to the council, where some have tried and none have conquered. More curious is the absence of any new wave of young, dedicated professionals eager to serve in political office here.

Many who might have entertained the idea of public service some years ago have found happiness, status and far better incomes in private business -- as lawyers, company executives, bankers, consultants. One successful lawyer who has been active in local Democratic politics, Robert B. Washington, notes that "many of us who came out of the civil rights movement used to look to government service as the next step. But today who needs that grief?" Others who also work the political scene from outside city hall say there is less idealism about what government can do and less desire to risk personal and family distress in a fishbowl constantly monitored by the local media.

"That's how people judge it," says City Administrator/Deputy Mayor Thomas Downs, one who has stayed on. "No status, no accolades, the risk of a personal reputation. You've got to be a masochist."

So it is that a number of highly regarded top officials have left city hall: former city administrator Elijah Rogers to private business, former corporation counsel Judith Rogers to a judgeship and others to various legal/consultant jobs.

There's another factor. At age 11, home rule in Washington hasn't nurtured either a two-party system of any consequence or any lively rivalries within the Democratic Party. With little history behind any of the elective offices, challengers either have not pinpointed incumbents' shortcomings or made the case for themselves. If Marion Barry is one beneficiary, so are incumbent council members who either have no significant opposition or a handful of opponents who split the votes and lose to the recognized name. The king of the reelecteds is not Barry, but Walter Fauntroy; nobody knows quite what a delegate to the House should be doing in the first place.

Barry seems to thrive on all this -- and he might as well, because he's got no higher office to run for. The danger in this political dead end is executive boredom and casual management -- which can be interpreted by some subordinates as an invitation to take personal advantage of their public positions. It also can rob the voters of a good chance to bring the mayor out for debate, for criticism -- and for a good scare.

After all, how full of energy and vision might Barry be in his 12th year as mayor? Or his 16th? At this point, he's only looking ahead at 16 weeks -- with a smile.