Many people in Jackson, Mich., Jackson, Miss., and Jackson, Tenn., are reading about the elections in Washington and wondering what the elections mean. I can tell them that a new day is dawning.

A woman named Sharon Pratt Dixon, an underdog who used a shovel to symbolize her vow to scoop this city clean, is almost certain to replace Marion Barry as the new mayor of this marvelous city of monuments and magnolias, of political dogs and gorgeous dogwoods.

Dixon will work with a D.C. Council with a new chairman and new council members; she'll have a chance to purge a police force that has been party to myriad scandals. She'll have people fighting the drug scourge who are not themselves part of the drug culture, as was the case with lame-duck Mayor Marion Barry.

Despite the celebrity of Barry's trial on drug charges, the larger problem of this city has been that it has too many people on the payroll who don't do anything -- meaning it can take four hours to renew your driver's license -- who don't do anything with courtesy and competence and who do nothing better than the often-illegal biddings of the top official who gave them a job and have for years cast their votes for their sugar daddies. A dual problem is that this city has been ripped off by the awarding of millions of dollars in contracts issued on the basis of sexual favors, drug deliveries, cronyism, nepotism and every outrage known to bad governments.

Can Sharon Pratt Dixon, who scored such a stunning upset, wipe out problems that seem to have become endemic in the Barry administration? She has the advantage of being able to start early, because she doesn't have to worry about being defeated by former police chief Maurice Turner in the November elections. Turner is a Republican, and his running for mayor of D.C. is like an Israeli general running for mayor of Baghdad. Worse yet, Turner was police chief when crooks dropped most of the stuff that Dixon pledges to shovel clean.

Don't expect this physically beautiful, even majestic, city to become a crime-free, drug-free, corruption-free place in a month or a year. Dixon lacks experience. Eleanor Holmes Norton, this colony's likely new nonvoting delegate to Congress, will carry the heavy baggage of disrespect for her failure to pay D.C. income taxes in one year and even to file returns in seven other years.

The national economic outlook of crippling budget deficits, cuts in social programs for the poor, a neglect of education for the masses and perhaps even the outrageous cost of a war in the Persian Gulf area should make it clear that every city in America is in for hard times. Washington can never be an exception. A drug cartel that dismays people in Boston demolishes those of us who live on the banks of the Potomac.

But Washington is coming back. Voters in Washington who were deemed to be the suckers of political demagogues who used racist appeals to their anger and frustrations turned out Tuesday to be damned independent -- and discerning for the most part.

I don't want to lay a burden of impossible expectations on Dixon. After all, if drug czar William Bennett has not shut down the cocaine cartels of Colombia with all the resources of gun power and money that he has, we can't expect a lady with no great military and financial resources to transform this city into a "drug-free zone" with a wave of her pinkie.

But we do have new hope here. I hope that elections will soon produce higher expectations in dozens of other cities that have been wallowing in doldrums created by dope and duplicity on the part of the people elected to make our cities better.