With luck, the registered voters of the District of Columbia--or people who thought they were registered in D.C.--will soon be able to look themselves up on a list published by the D.C. Board of Elections.

The list, pulled together with the aid of computer specialists from GEICO insurance, will probably have something in excess of 250,000 names on it. It will probably be published in legal fashion in the pages of this newspaper. People who think they should be on the voter roll and don't see their names presumably will be able to correct the matter well in advance of September's election. And, presumably, city election officials will begin to cull from the roll names that should no longer be there.

What a small thing, this list. And yet it will be one of the most dramatic steps forward ever taken by the District government. You marvel at the beauty and simplicity of such a list; you also ask: what took the city so long to compile it?

Washington has a number of satellite counties and communities that register voters and hold elections with a minimum of fuss and bother. Why can't Washington?

The city, for reasons good and true, resents carping views from the outside that suggest it doesn't know how to conduct its own affairs. This second-guessing from the sidelines can be nettlesome at times (as when a commuter tax is dismissed out of hand), worth listening to at others (why can't the water bills be straightened out?)

But when it comes to the matter of holding elections, the issue is clear. The conduct of an election--everything from signing up and keeping track of registered voters to the actual vote count itself--testifies to the basic integrity and efficiency of the city management. After all, home rule was largely about voting, selecting the people who are vested with real power and authority to run the city. If that basic selection process is still in doubt after eight years of home rule--and it is-- how is the city to maintain credibility, not only in the eyes of skeptical outsiders, but in the view of its own citizens?

History cannot be changed, and the city is, it seems, finally on its way toward sorting out the election mess. But it is not encouraging that it took a newspaper editorial and a voluntary effort on the part of a private company to put the city on the road to electoral responsibility.

The city is surrounded by jurisdictions that do a creditable job of keeping track of their voters. Call the Fairfax County office, for instance, and you get a quick, efficient yes, you're registered and eligible for the next election, you vote at such-and-such a location, and have a good day.

There appear to be few mysteries as to how these things work. Shouldn't the city have checked out the methods used in the suburbs? Couldn't it have hired its own computer expert to straighten out the city system--and the people who run it-- without waiting for the GEICO cavalry to ride to the rescue?

Couldn't the city, in short, have realized without being told that there was a missing, vital cog in its administrative machinery and taken steps to replace it?