DEMOCRAT ANDREW P. MILLER'S request for a recount of Virginia's Senate race may be based mainly on die-hard hope. Mr. Miller has pointed out some small oddities in the certified returns, which show that Republican John W. Warner won by 4,721 votes out of 1.2 million. That margin is so slight -- four-tenths of one percent -- that a two-vote gain for Mr. Miller in each of the state's 1,857 precincts would give him the seat. The problems mentioned so far, however, do not appear to be that consequential. A new tally may well change the numbers a bit without changing the results.

Regardless of its outcome, a court-supervised recount is useful. When an election is so close, voters as well as candidates benefit from extra assurance that the result is accurate. Virginia law recognizes this by enabling losing candidates to request a recount, without showing fraud or error, whenever the margin is less than one percent. And since a statewide recount has never occurred before, this one will also serve as a unique audit of state and local vote-counting processes.It will flag any problems that do exist.

Because the situation is unprecedented, the court's first job is to decide how to proceed -- and thus how much money and time will be involved. The cost estimate by the state board of elections -- around $120,000 -- seems to assume that different people must check each precinct. That seems extravagant, as the Miller team has noted, because many jurisdictions have stored all of their voting machines safely in one place. One set of checkers could review a batch of precincts without even changing sites. Mr. Miller does have a special interest in keeping down the cost, because the law requires him to pay for the recount if he loses it. (If he wins, the state will pay.) But the court should recognize that efficient, economical procedures are in the public interest, too, no matter who foots the bill.

This points to a policy problem that the General Assembly should address. The pay-if-you-lose rule was adopted some time ago to discourage frivolous challenges. However, it contradicts the law's sound premise that recounts of close elections are not frivolous. Surely a candidate's ability to have such results verified -- whether or not he winds up winning -- should not turn on his ability to pay. The commonwealth should bear the official costs.

The legislature should try, too, to speed up the whole post-election process. By now, a lot of people may think that Mr. Miller is just dragging things out. In fact, the official results were not certified, and could not be scrutinized by anyone, until Nov. 27 -- the date set by law. Getting the rural returns to Richmond might have taken that long in horse-and-buggy days, but surely now the pace could be picked up.