Marion Barry won the crucial Democratic nomination for mayor in 1978 with 34 percent of the vote in a close three-way primary, leaving him open to criticism that he lacked a full-fledged mandate from the voters. The healing process was a long one.

This election year, there are eight Democrats running, and it is possible that a candidate with even less of a popular mandate could become the Democratic nominee in a town where 75 percent of the registered voters are Democrats.

"It's very clear that there is a need for a system to allow the party to choose from two major candidates and not a field of eight or nine," said Theodis R. Gay, the D.C. Democratic chairman. "In order to govern effectively a mayor needs to have a majority of the voters."

So Gay is forming a task force to consider alternatives to the straight primary election procedure for choosing the party's nominee, and D.C. Council Chairman Arrington Dixon has introduced legislation to require a runoff election when no candidate for mayor or council gets more than 40 percent of the primary vote. The runoff would be held within 21 days of the primary.

Dixon's bill is still before the government operations committee and is expected to go nowhere for a while. Too many incumbents have been nominated in close elections, including the committee's chairman, William R. Spaulding.

John L. Ray, (D-At-large) and a candidate for mayor, is proposing that the council enact emergency legislation that would create a runoff election for this year's primary. "It's ridiculous to have a mayor elected with 30 percent of the vote," says Ray.

Gay agrees with Ray and Dixon that the system should be changed, but has a different view on who should change it. "The party controls its elections," he says. "Not the City Council. Not the courts. No amount of emergency legislation is going to change that."

Gay says he is not wedded to a runoff as the only way change the procedure. There could be a preferential voting system in which voters would rank various candidates and, to begin with, the candidates who get the least first-place votes would be eliminated. Candidates who came in second on ballots where losing candidates received first-place votes would have those second-place votes turned into first-place votes until one candidate had more than 50 percent of the first-place votes and thereby was nominated.

A second idea is approval voting, according to Gay. Under that plan voters would vote for all the candidates they think are capable of doing the mayor's job. The candidate with the highest number of approval votes would win.

A third alternative would permit the party to choose candidates for the primary through either a party convention or a party caucus. In Virginia, Democrats and Republicans actually choose the party nominee for statewide offices through conventions.

"What I'd like to see someday," said Gay, "is the party having a platform and measuring the candidates against the platform. The system we have now is based on personalities. . . . People were attached to [former mayor] Walter Washington or [D.C. Del.] Walter Fauntroy, not to the party. I'd like to see that turned around. . . . I'd like to see people come into the party and work their way up to becoming candidates for major offices."

The major Democratic candidates for mayor this year have varying reactions to the plan to change the primary system. Barry says he hasn't thought about it. Ray would like to have the runoff this year. Council Member Charlene Drew Jarvis (D-Ward 4) is for the plan, but only if, she says with a laugh, "the top three candidates are in the runoff."

At-large Council Member Betty Ann Kane is opposed. "Some people don't remember it, but we had runoffs in this town," said Kane. "What happened when we had the runoffs in the 1968 D.C. School Board election was that we had a very small turnout. It was appalling."

Patricia Roberts Harris, a former Democratic National Committeewoman from the city and Carter administration Cabinet member, says she likes the idea--but not for the current election. "At this stage I don't propose any changes in the law," she says. "I only hope they can count. I will talk about a runoff after I have become mayor."

One man with a strong interest in not having the runoff is Albert Beveridge, chairman of the D.C. Board of Elections and Ethics.

"We have too many damn elections in this city," he said. "We have two this year (the primary and the general), one next year (school board) and then three in '84 (presidential primary in May, a September primary for the council and a November general election). With a runoff, that would mean extra elections. We have enough problems with the current system and we already have to run two elections this year. Three elections would be a strain on the system."